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TRIPLES: Applications Of Pythagorean Triples

By Kenneth R. Williams

India: Motilal Banarsidass. 2005. First Thus Private Press. H Hardcover. New. 168P. This book shows an original and highly effective way of unifying many branches of mathematics using Pythagorean triples and Vedic Maths. A simple, elegant method for combining these triples gives unexpected and powerful general methods for solving a wide range of mathematical problems. There are applications in trigonometry (you do not need any of those complicated formulae), coordinate geometry (2 and 3 dimensions), transformations (2 and 3 dimensions), simple harmonic motion, astronomy etc. Contents: 1 TRIPLES: The Triple Theorem; Some Historical Background; Notation for Triples; Equal, Prime and Complementary; Triples; Some Perfect Triples;2 TRIPLE ARITHMETIC; Addition of Triples; Double Angle; Triple Subtraction; Quadrant Angles; Triple Geometry; Angles of 30, 60, 45 etc.; Half Angle; Simplifying Calculations; Summary. 3 TRIPLE TRIGONOMETRY: Introduction; Inverse Functions; The General Triple; Solution of Trigonometrical Equations; Further Trigonometrical Equations- A; Further Trigonometrical Equations- B; Further Trigonometrical Equations- C. 4 TRANSFORMATIONS IN A PLANE: Transposition of the Origin; Rotations; Spirals; Integration of cosx etc.; Rotation of Lines and Curves; Reflections. 5 COORDINATE GEOMETRY: Length of Perpendicular; Foot of Perpendicular; Angle between Two Lines; Equation of a Line; Further Examples. 6 CODE NUMBERS: Grouping Triples; Code Numbers; Geometrical Significance of the Code Numbers; Code Number Pairs; Code Numbers as Triples; Algebraic Formulation; Converting Code Numbers to Triples; Converting Triples to Code Numbers; Addition and Subtraction of Code Numbers; Code Numbers of Code Numbers; Code Numbers of Complementary Triples; Code Numbers of Supplementary Triples; Code Numbers for 0, 90, 180, 270; Relation between Code Numbers and Angles; Further Examples; Summary. 7 SOLUTION OF TRIANGLES: Angle Deficiency Formula; The Sine Formula; The Code Number Formula.8 FURTHER APPLICATIONS OF TRIPLES: Solution of Equations; Complex Numbers; Conics; Difference and Sum of Squares; Incircles and Circumcircles; The Golden Triple; 9 ANGLES IN PERFECT TRIPLES: Revision; Triples and Their Angles; Finding the Angle in a Given Triple; Further Applications of Code Numbers; Finding a Triple with a Given Angle; A Refinement.10 SINE, COSINE, TANGENT & INVERSES: Sine, Cosine and Tangent; Inverse Cosine and Inverse Sine; Inverse Tangent.11 HYPERBOLIC FUNCTIONS: Addition and Subtraction; Double Angle; Equations. 12 APPLIED MATHS APPLICATIONS: Simple Harmonic Motion; Projectiles; Forces in Equilibrium; Work Done by a Force and Moment of a Force. 13 THE TRIPLE METHOD: Range of Application; Deriving the Conventional Formulae; Two Comparisons of the Conventional and Triple Methods. 14 QUADRUPLES: Introduction; Quadruple Generators; Obtaining the Code Numbers of a Perfect Quadruple; The Coordinate Axes; Quadruple Subtraction; Comparative Densities of Perfect Triples and Quadruples. 15 APPLICATIONS OF QUADRUPLES: Coordinate Geometry; Work and Moment; Rotation about Coordinate axis; 3-Dimensional Rotation of Curves; Rotation Conicoids. 16 QUADRUPLES IN ASTRONOMY: Addition of Perpendicular Triples. Change of Coordinate System; Quadruples and Orbits; Quadruple for given i, A; Inclination of Orbit; Quadruple Subtraction;. Quadruple Addition; Doubling and Halving a Quadruple; Code Number Addition and Subtraction; Angle in a Quadruple; Angular Advance; Relationship between d, A; To Obtain a Quadruple with a Given Inclination. PROOFS. ANSWERS TO EXERCISES. REFERENCES. INDEX OF VEDIC FORMULAE. INDEX.

$28.75

Vedic Math Teachers Manual, Volume 2, Intermediate

By Kenneth Williams

India: Motilal Banarsidass. 2005. F First Edition. H Hardcover. New. 2003. Contents:PREFACE LESSON 1 Basic Devices Introduction Digit Sums Left to Right Addition Multiplication Advantages of left to Right Calcn Writing Left to Right Sums Checking Devices Subtraction Subtraction from Left to Right Checking Subtraction Sums LESSON 2 MORE BASIC DEVICES Number Splitting Addition 14 / Subtraction Multiplication 16 / Division All from 9 and the Last from 10 Subtraction from a Base Calculations Involving Money First Extension Second Extension Combining the Extensions Bar Numbers Advantages of Bar Numbers General Subtraction LESSON 3 SPECIAL METHODS Proportionately Doubling and Halving Extending the Multiplication Tables Multiplying by 5, 50, 25 All from 9 and the Last from 10: Multiplication Numbers just below 100 Geometrical Proof Algebraic Proof Other Bases Numbers above the Base One Number ABOVE and one below the Base Proportionately Multiplying Numbers near Different Bases Squaring Numbers near a Base Mental Calculations Special methods LESSON 4 BY ONE MORE THAN THE ONE BEFORE Special Multiplications Squaring Numbers that End in 5 A Variation Multiplication Summary Recurring Decimals Denominator Ending in 9 Proof A Short Cut Proportionately Longer Numerators LESSON 5 AUXILIARY FRACTIONS Auxiliary Fractions: First Type Denominators Ending in 8, 7, 6 Auxiliary Fractions: Second Type Denominators Ending in 1 Alternative Method Denominators Ending in 2, 3, 4 Working 2, 3 etc. Figures at a Time LESSON 6 VERTICALLY AND CROSSWISE Fractions Adding & Subtracting Fractions Proof A Simplification Comparing Fractions Multiplication and Division General Multiplication Revision Multiplying 2-Figure Numbers Explanation Explanation of earlier special method The Digit Sum Check Multiplying 3- Figure Numbers Moving Multiplier Algebraic Multiplications The Digit Sum Check Three-Figure Numbers Four-Figure Numbers Writing Left to Right Sums From Right to Left setting the sums out Using Bar Numbers LESSON 7 SQUARES AND SQUARE ROOTS General Squaring Two-Figure Numbers Number Splitting Algebraic Squaring Squaring Longer Numbers Written Calculations – Left to Right Written Calculations – Right to Left Square Roots of Perfect Squares LESSON 8 SPECIAL MULTIPLICATION METHODS Special Numbers Repeating Numbers Proportionately Disguises Using the Average PROOF Multiplication by Nines Multiplication by 11 Percentages Increasing Reducing LESSON 9 TRIPLES Definitions Triples for 45°, 30° and 60° Triple Addition Double Angle Variations of 3,4,5 Quadrant Angles Rotations LESSON 10 SPECIAL DIVISION Division by Nine Adding Digits A Short Cut Dividing by 8 Algebraic Division Dividing by 11, 12 etc. Larger Divisors Divisor just Below a Base A Simplification Divisor just Above a Base Proportionately LESSON 11 STRAIGHT DIVISION Single Figure on the Flag Short Division Digression Longer Numbers Multiplication Reversed Decimalising the Remainder Negative Flag Digits Larger Divisors ALGEBRAIC DIVISION LESSON 12 EQUATIONS Linear One x Term Two x Terms Quadratic Equations Simultaneous Equations By Addition and By Subtraction A Special Type General Method Another Special Type LESSON 13 APPLICATIONS OF TRIPLES Triple Subtraction Triple Geometry Angle Between Two Lines Half Angle Coordinate Geometry Gradients Circle Problems Length of Perpendicular LESSON 14 SQUARE ROOTS Squaring Square Root of a Perfect square Preamble Two-Figure Answer Reversing Squaring Three-Figure Answer Reversing Squaring General Roots Changing the Divisor Heuristic Proof LESSON 15 DIVISIBILITY Elementary Parts The Ekadhika Osculation Explanation Testing Longer Numbers Other Divisors The Negative Osculator LESSON 16 COMBINED CALCULATIONS Algebraic Arithmetic Pythagoras Theorem SUTRAS AND SUB-SUTRAS 9-POINT CIRCLES REFERENCES INDEX OF THE VEDIC FORMULAE INDEX .

$34.50

Vedic Math Teachers Manual, Volume 3, Advanced

By Kenneth Williams

India: Motilal Banarsidass. 2005. F First Edition. H Hardcover. New. Contents:PREFACE LESSON 1 LEFT TO RIGHT CALCULATIONS 1.1 INTRODUCTION 1.2 ADDITION 1.3 MULTIPLICATION Advantages OF LEFT TO RIGHT CALCULATION 1.4 WRITING LEFT TO RIGHT SUMS 1.5 SUBTRACTION 1.6 DIGIT SUMS 1.7 CHECKING DEVICES CHECKING SUBTRACTION SUMS 1.8 ALL FROM 9 AND THE LAST FROM 10 1.8a SUBTRACTION FROM A BASE 1.8b BAR NUMBERS ADVANTAGES OF BAR NUMBERS 1.8c GENERAL SUBTRACTION LESSON 2 SPECIAL METHODS 2.1 MULTIPLICATION NEAR A BASE 2.1a Numbers just below the base 2.1.b Above the base 2.1c Above and below 2.1d Proportionately 2.1e With different bases 2.2 MENTAL CALCULATIONS 2.3 SPECIAL NUMBERS 2.3a Repeating numbers 2.3b Proportionately 2.3c Disguises 2.4 DIVISION BY NINE 2.4a Adding Digits 2.4b A Short Cut 2.4c Dividing by 8 2.4d Algebraic Division 2.4e Dividing by 11, 12 etc. LESSON 3 RECURRING DECIMALS 3.1 DENOMINATOR ENDING IN 9 3.2 A SHORT CUT 3.3 PROPORTIONATELY 3.4 LONGER NUMERATORS 3.5 DENOMINATORS ENDING IN 8, 7, 6 3.6 DENOMINATORS ENDING IN 1 3.7 DENOMINATORS ENDING IN 2, 3, 4 3.8 WORKING 2, 3 ETC. FIGURES AT A TIME LESSON 4 TRIPLES 4.1 Definitions 4.2 Triples for 45°, 30° and 60° 4.3 Triple Addition 4.4 Double Angle 4.5 Variations of 3,4,5 4.6 Quadrant Angles 4.7 Rotations LESSON 5 GENERAL MULTIPLICATION 5.1 TWO-Figure Numbers Explanation/ The Digit Sum Check 5.2 Moving Multiplier 5.3 Algebraic PRODUCTS The Digit Sum Check 5.4 Three-Figure Numbers 5.5 Four-Figure Numbers 5.6 Writing Left to Right Sums 5.7 From Right to Left setting the sums out 5.8 Using Bar Numbers LESSON 6 SOLUTION OF EQUATIONS 6.1 TRANSPOSE AND APPLY 6.1a SIMPLE EQUATIONS 6.1b MORE THAN ONE X TERM 6.2 SIMULTANEOUS EQUATIONS 6.2a GENERAL SOLUTION 6.2b Special Types 6.3 QUADRATIC EQUATIONS 6.4 ONE IN RATIO THE OTHER ONE ZERO 6.5 MERGERS 6.6 WHEN THE SAMUCCAYA IS THE SAME IT IS ZERO 6.6a Samuccaya as a common factor 6.6b Samuccaya as the Product of the Independent Terms 6.6c Samuccaya as the Sum of the Denominators 6.6d Samuccaya as a Combination or Total Proof/ EXTENSION 6.6e other typeS 6.7 THE ULTIMATE AND TWICE THE PENULTIMATE 6.8 ONLY THE LAST TERMS 6.9 SUMMATION OF SERIES 6.10 FACTORISATION LESSON 7 SQUARES AND SQUARE ROOTS 7.1 Squaring 2-FIGURE NUMBERS 7.2 Algebraic Squaring 7.3 Squaring Longer Numbers 7.4 Written Calculations 7.4a Left to Right 7.4b Right to Left 7.5 Square Roots of Perfect Squares LESSON 8 APPLICATIONS OF TRIPLES 8.1 Triple Subtraction 8.2 Triple Geometry 8.3 Angle Between Two Lines 8.4 Half Angle 8.5 Coordinate Geometry 8.5a Gradients 8.5b Length of Perpendicular 8.5c Circle Problems 8.5d EQUATION OF A LINE 8.6 COMPLEX NUMBERS CONTENTS LESSON 9 DIVISIBILITY 9.1 Elementary Parts 9.2 The Ekadhika 9.3 Osculation Explanation 9.4 Testing Longer Numbers 9.5 Other Divisors 9.6 The Negative Osculator 9.7 OSCULATING WITH GROUPS OF DIGITS LESSON 10 STRAIGHT DIVISION 10.1 Single Figure on the Flag 10.2 Short Division Digression 10.3 Longer Numbers Multiplication Reversed 10.4 Decimalising the Remainder 10.5 Negative Flag Digits 10.6 Larger Divisors 10.7 ALGEBRAIC DIVISION LESSON 11 SQUARE ROOTS 11.1 Squaring 11.2 Square Root of a Perfect square 11.2a Preamble 11.2b Two-Figure Answer Reversing Squaring 11.2c Three-Figure Answer Reversing Squaring 11.3 General Square Roots 11.4 Changing the Divisor Heuristic Proof 11.5 ALGEBRAIC SQUARE ROOTS LESSON 12 TRIPLE TRIGONOMETRY 12.1 COMPOUND ANGLES 12.2 INVERSE FUNCTIONS 12.3 THE GENERAL TRIPLE 12.4 TRIGONOMETRIC EQUATIONS 12.4a SIMPLE EQUATIONS 12.4b A SPECIAL TYPE LESSON 13 COMBINED OPERATIONS 13.1 Algebraic 13.2 Arithmetic 13.2a SUMS OF PRODUCTS 13.2b ADDITION AND DIVISION 13.2c STRAIGHT DIVISION 13.2d MEAN AND MEAN DEVIATION 13.2e DIVIDING SUMS OF PRODUCTS 13,2f VARIANCE 13.3 Pythagoras’ Theorem LESSON 14 SOLUTION OF POLYNOMIAL EQUATIONS 14.1 QUADRATIC EQUATIONS 14.1a x > 1 PROOF 14.1b x 1 14.1e –1 < x < 0 14.1f x LARGE 14.2 HIGHER ORDER EQUATIONS 14.2a CUBE ROOT 14.2b CUBIC EQUATIONS A SIMPLIFICATION A CUBIC WITH 0 < x< 1 14.2c QUINTICS LESSON 15 CALCULUS METHODS 15.1 PartialF

$40.25

ASTRONOMICAL APPLICATIONS OF VEDIC MATHEMATICS

By Kenneth Williams

www.sacredscience.com Sacred Science Institute. H Hard Cover. New. As NEW. Science 139p. Contents: Introduction to Vedic Mathematics. Prediction of Eclipses: Prediction of the Times Of Contact of the Moonís Penumbral and Umbral Shadows With the Earth. Partial Phase. Total Phase. Approximate Position of the Eclipse Path. Time of Total Eclipse For an Observer on Earth. Besselís Method, Early Eclipse Prediction, Solution of Eclipse Equation. Keplerís Equation: A Transcendental Equation, Solution of Keplerís Equation. Introduction to Triples: Notation & Combination, Triple Addition, Quadrant Triples, Rotations, Subtraction, Half-Angle Triple. Triple Code Numbers, Angles in Perfect Triples. Prediction of Planetary Positions: Heliocentric Position, Mean Anomaly, Geocentric Position, Geocentric Longitude, Geocentric Correction, Planet Finder. Spherical Triangles Using Triples: Triple Notation & Formulae for Spherical Trigonometry, Cosine Rule to Find an Angle, Sine Rule to Find Angle, Cotangent Rule to Find Angle, Polar Cosine Rule. Right Angled Spherical Triangles. Spherical Triangles Using Code Numbers. Determinants. Quadruples. Addition of Perpendicular Triples, Rotation About A Coordinate Axis. Quadruples & Orbits, Inclination of Orbit, Angle Between Two Directions. Inclination of Planetary Orbits. Calculation of Radius Vector.

$28.75

Vedic Math Teachers Manual, Volume 1, Elementary

By Kenneth Williams

India: Motilal Banarsidass. 2005. F First Edition. H Hard Cover. New. Contents:PREFACE;LESSON 1 COMPLETING THE WHOLE;Introduction The Ten Point Circle; Multiples of Ten; Deficiency from Ten; Deficiency and Completion Together Mental Addition; Completing the Whole; Columns of Figures; By Addition and By Subtraction; Subtracting Numbers Near a Base; LESSON 2 DOUBLING AND HALVING: Doubling; Multiplying by 4, 8 Halving; Splitting Numbers; Dividing by 4, 8; Extending your Tables; Multiplying by 5, 50, 25 Dividing by 5, 50, 25; Dividing by 5; Dividing by 50, 25; LESSON 3 DIGIT SUMS: Adding Digits; The Nine Point; Circle; Casting out Nines; Digit Sum Puzzles; More Digit Sum Puzzles; The Digit Sum Check Multiplication Check; The Vedic square; Patterns from the Vedic Square; Number Nine; LESSON 4 LEFT TO RIGHT: Addition: Left to Right; Multiplication: Left to Right; Doubling and Halving; Subtraction: Left to Right; Checking Subtraction Sums; More Subtractions; LESSON 5 ALL FROM 9 AND THE LAST FROM 10: All From 9 and the Last from 10; Subtraction Adding Zeros; One Less; One More; One Less Again; Money LESSON 6 NUMBER SPLITTING: Addition; Subtraction; Multiplication; Division; LESSON 7 BASE MULTIPLICATION: Times Tables; Numbers just Over Ten; Multiplication Table Patterns; Recurring Decimals; Numbers Close to 100; Mentally; Numbers Over 100 Mental Maths; Russian Peasant; Multiplication; Larger Numbers; Numbers Above the Base; Proportionately; Another Application of Proportionately; Multiplying Numbers near Different Bases; Squaring Numbers near a Base; A Summary. LESSON 8 CHECKING AND DIVISIBILITY Digit Sum Check for Division The First by the First and the Last by the Last The First by the First The Last by the Last Divisibility by 4 Divisibility by 11 Remainder after Division by 11 Another Digit Sum Check LESSON 9 BAR NUMBERS Removing Bar Numbers All from 9 and the Last from 10 Subtraction Creating Bar Numbers Using Bar Numbers LESSON 10 SPECIAL MULTIPLICATION Multiplication by 11 Carries Longer Numbers By One More than the One Before Multiplication by Nines The First by the First and the Last by the Last Using the Average Special Numbers Repeating Numbers Proportionately Disguises LESSON 11 GENERAL MULTIPLICATION Revision Two-Figure Numbers Carries Moving Multiplier Extension Multiplying Binomials Multiplying 3-Figure Numbers Written Calculations LESSON 12 SQUARING Squaring Numbers that end in 5 Squaring Numbers Near 50 General Squaring The Duplex Number Splitting Algebraic Squaring Digit Sums of squares Square Roots of Perfect Squares 3 and 4 Figure Numbers LESSON 13 EQUATIONS One-step Equations Two-step Equations Three-step Equations LESSON 14 FRACTIONS Vertically and Crosswise A Simplification Comparing Fractions Unification of Operations LESSON 15 SPECIAL DIVISION Division by 9 Longer Numbers Carries A Short Cut Division by 8 etc. Division by 99, 98 etc. Divisor Below a Base Number Two-Figure answers Divisor Above a Base Number LESSON 16 THE CROWNING GEM Single Figure on the Flag Short Division Digression Longer Numbers Negative Flag Digits Decimalising the Remainder; SUTRAS AND SUB-SUTRAS;9-POINT CIRCLES; REFERENCES;INDEX OF THE VEDIC FORMULAE;INDEX.

$34.50

THE COSMIC COMPUTER COURSE, BOOK 1

By Kenneth R. Williams & Mark Gaskell

www.sacredscience.com Sacred Science Institute. 2006. Deluxe Hardcover Facsimile Edition Privately Printed. H Hard Cover Maroon Suede Guilt. New. 250P. Each of the three books has 27 chapters each of which is prefaced by an inspiring quote from a famous mathematician, philosopher etc. Also in each book there are historical notes which relate to the authors of the quotes, a list of Sutras and three other short but interesting sections (e.g. Pascal's Triangle,Vedic Maths, Fractals). Written for 11-14 year old pupils (some of the material in Books 1 and 2 is suitable for children from the age of about eight) this course covers the National Curriculum for England and Wales, but is also the perfect course for anyone who wants to develop a thorough understanding of Vedic Mathematics. This full course consists of the Textbook, the Teacher's Guide and the Answer Book. Book 1 deals mainly with basic arithmetic, proportion, decimals, basic algebra and geometry, polygons, area, volume etc. For detailed contents see the Expedient Learning Portal

$51.75

THE NEW DRAWING ON THE RIGHT SIDE OF THE BRAIN
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THE NEW DRAWING ON THE RIGHT SIDE OF THE BRAIN

By Betty Edwards

1999. H Hardcover. New. 320pp. This book is amazing! It will teach anyone who feels that they draw like a child to learn to draw stunningly realistic drawings within the time it takes to work through the book(about a month). An superb example of true education, showing that everyone possesses the inherent ability express their vision through drawing, and that our lack of this ability is solely due to our lack of know-how, received through the poor or non- existent art education given in our schools. Book Jacket: ìTranslated into thirteen languages, with more than 2.5 million copies sold, Drawing on the Right Side of the Brain is the world's most widely used drawing instruction book."--BOOK JACKET. "This twentieth-anniversary edition of Drawing on the Right Side of the Brain has been dramatically revised, with more than fifty percent new material, including: recent developments in brain research that relate to drawing; new insights on the use of drawing techniques in the corporate world and in education; instruction on self- expression through drawing; ways to step beyond black-and-white drawing into color; and detailed advice on applying the five basic skills of drawing to solve problems." Contents: 1Drawing and the Art of Bicycle Riding. 2 The Drawing Exercises: One Step at a Time. 3 Your Brain: The Right and Left of It. 4 Crossing Over: Experiencing the Shift from Left to Right. 5 Drawing on Memories: Your History as an Artist. 6 Getting Around Your Symbol System: Meeting Edges and Contours. 7 Perceiving the Shape of a Space: The Positive Aspects of Negative Space. 8 Relationships in a New Mode: Putting Sighting in Perspective. 9 Facing Forward: Portrait Drawing with Ease. 10 The Value of Logical Lights and Shadows. 11 Drawing on the Beauty of Color. 12 The Zen of Drawing: Drawing Out the Artist Within. Afterword: Is Beautiful Handwriting a Lost Art?.

$34.50

AN HISTORICAL SURVEY OF THE ASTRONOMY OF THE ANCIENTS

By Sir George Cornewall Lewis

Todd Pratum. 2004. Privately Printed. H Hardcover. New. Original 1862 London. 527p. This new high quality cloth reproduction of the original edition is a new experiment in producing high quality reprints of some of the older important books. This is NOT one of our spiral bound reprints, but a beautiful new hardcover book by Pratum Books. Selected Contents: Primitive Astronomy of the Greeks & Romans; Greek World Conception; Solar Year; Lunar Year & Month; Discordance of Greek Calendars; Carian, Acarnanian & Arcadian Years; Short Egyptian Year; Roman Year; Fixed Stars; Early Divination; Philosophical Astronomy of the Greeks from Thales to Democritus; Origin of Astronomy in Greece; Eclipse of Thales; Solon’s Reform of Athenian Calendar; Astronomical Doctrines of Anaximander, Anaximenes, Heraclitus, Xenophanes; Parmenides, Empedocles, Anaxagoras, Diogenes of Apollonia, Socrates, Meton, Leucippus, Democritus; Trieteric & Octaeteric Intercalary Cycles; Astronomical Speculations of Pythagoras & His School; Philolaic System of the Universe; Pythagorean Cycles; Scientific Astronomy of the Greeks from Plato to Eratosthenes; Hypothesis of Planetary Motions; Astronomical Doctrines of Aristotle, Callippus, Hicetas, Ecphantus, Theophrastus, Eudemus, Autolycus, Euclid, Aristarchus, Archimedes, Aristyllus; Measures of Daily Time; Rotation of Earth on its Axis; The Phaenomena of Euclid; Heliocentric System of Aristarchus; Alexandrine School of Astronomers; Timaeus & The Motion of the Earth; On the Dials of the Ancients; Prediction of Eclipses; Uniform Calendar & Religious Festivals; Roman Measures of Time; Order of the Planets, Revolution of Inferior Planets Around Sun; Ptolemy; Geocentric System; Astronomy of Babylonians & Egyptians; Origin of Astronomical Observation; Chaldean & Egyptian Priests as Astronomical Observers; Egyptian Solar Year; Egyptian Astronomy Passed to Greece; Length of Egyptian Year; The Canicular or Sothiac Period; Astrological Divination of Chaledeans; Origins of Astrology; Early History & Chronology of Egyptians; Plato’s Chronology; Early History & Chronology of Assyrians; Babylonian History; Nineveh & Babylon; Astronomical Canon; Evidence of Age of the World; Navigation of the Phoenicians; Phoenicians Originators of Astronomy.

$69.00

PHOTOREADING: Whole Mind System
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PHOTOREADING: Whole Mind System

By C. Paul R. Scheele

Minnesota Learning Strategies Corp.. 1999. S Soft Cover. New. 165p. We consider this to be the most promising speed reading system that we have seen so far. It teaches the reader to approach a book from several narrowing perspectives, developing a quick and full overview of the work. Scheele then shares the techniques of "PhotoReading" where one scans the entire book with an unfocused gaze in order to transfer it photographically into the right brain. He follows up with the development of recall of this memory, along with continued closer analysis of the book as needed. Very promising as a tool to digest and integrate large amounts of information. Third edition. Binding is Softbound.

$25.30

THE NATURAL CALCULATOR: Using The Natural Processes Of The Mind For Mental Calculations

By Kenneth R. Williams

India: Motilal Banarsidass. H Hardcover. New. 102 Pages. In this book the emphasis is on mental calculation, mainly mental multiplication, but addition, subtraction and division are also covered. Each chapter focuses on one Vedic formula and shows various ways in which it can be used. There is a detailed introduction outlining the benefits of mental mathematics(Vedic Maths). Introduction; 1 On The Flag Calculating From Left To Right; 2 Proportionately Multiplication Devices Involving Doubling And Halving; 3 By One More Than The One Before Squaring Numbers That End In 5; A Special Type Of Multiplication; 4 The First By The First And The Last By The Last Calculating Checks; A Special Type Of Multiplication; 5 All From 9 And The Last From 10 Numbers Near A Base; Subtraction; Numbers Near Different Bases; Multiplying Three Numbers Simultaneously; Squaring Numbers Near A Base; Multiplication By 9's; Addition And Subtraction; 6 Vertically And Crosswise General Multiplication: Multiplying 2-Figure Numbers, 3-Figure Numbers, Moving Multiplier Method, 3 And 4-Figure Multiplication; General Squaring; Division- Divisor Near A Base; General Division; 7 Using The Average Products Using An Average; 8 By Addition And By Subtraction Squares From Squares; Products From Products; 9 By Mere Observation Use Of Special Numbers; Proofs; References; Answers.

$28.75

THE CIRCLE REVELATION

By Andrew P. Nicholas

England: Inspiration Books. F First Edition. S Soft Cover. New. 221p. This fascinating book is the most popular, simple and direct introduction to rapid geometry techniques and calculations developed from Vedic Maths, a popularized version of "Geometry For an Oral Tradition", listed below. It is a delightful read which will completely reorientate one's vision and understanding of Geometry within as little as a few hours. The approach is ideally suited to the twenty-first century, when audio-visual forms of communication are likely to be dominant. Contents: Angles, Triangles & Quadrilaterals; Properties of a Circle; Multiplication & Area; Parallels & Parallelograms; Similar Triangle' Equality & Equations; Number Arithemetic, Geometry & Algebra; Equal Areas & Similar Triangles; Further Properties of Circles; Pythagoras' Theorem; Proportion.

$28.75

THE COSMIC COMPUTER COURSE, BOOK 2

By Kenneth R. Williams & Mark Gaskell

www.sacredscience.com Sacred Science Institute. 2006. Deluxe Hardcover Facsimile Edition Privately Printed. H Hard Cover Maroon Suede Guilt. New. 250p. This full course consists of the Textbook, the Teacher's Guide and the Answer Book. Book 2 extends this, covering fractions, probability, sequences, negative numbers, percentages, equations, graphs, charts, transformations, bearings, Vedic Maths, etc.

$51.75

HOW TO THINK LIKE LEONARDO DA VINCI: Seven Steps to Everyday Genius
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HOW TO THINK LIKE LEONARDO DA VINCI: Seven Steps to Everyday Genius

By Michael J. Gelb

New York: Delacorte Press. 1998. F First Edition. H Hardcover. New. Science 322p. We suggest this title for a introduction to the more interesting modern day approaches to Expedient Learning, while tracing them back to the genius of Leonardo. This is an inspiring and inventive guide that teaches readers how to develop their full potential, using the principles of Da Vincian thought identified by the author. Beginning with a brief historical biography of Da Vinci and an overview of the astounding advances made in the arts and sciences during the Renaissance, Gelb illustrates the seven fundamental elements of Da Vinci's thought process: Questionare: A questing, insatiably curious approach to life Dimostrazione: A commitment to test knowledge through experience Sensazione: The continual refinement of the senses, especially sight, as the means to clarify experience Sfumato: A willingness to embrace ambiguity, paradox and uncertainty Arte/Scienza: The development of the balance between science and art, logic and imagination. "Whole-brain" thinking Corporalita: The cultivation of ambidexterity, fitness and poise Connessione: A recognition and appreciation for the interconnectedness of all things and phenomena. "Systems" thinking. Loaded with practical exercises, quotes, sidebars, illustrations and material drawn directly from Da Vinci's personal notebooks, How to Think Like Leonardo Da Vinci is both a tribute to his great achievements and a call to carry on his legacy in our everyday lives by utilizing our potential to the best of our ability.

$28.75

VERTICALLY AND CROSSWISE

By A. P. Nicholas, K. Williams, J. Pickles

Motilal Banarsidass, India. H Hard Cover. New. As NEW. Science 200P. This is an advanced book of sixteen chapters on one Vedic Maths Sutra, Vertically & Crosswise, ranging from elementary multiplication, etc. to the solution of non-linear partial differential equations. It deals with (i) calculation of common functions and their series expansions, and (ii) the solution of equations, starting with simultaneous equations and moving on to algebraic, transcendental and differential equations. The text contains exercises and answers. Contents: 1 Introduction To The Vertically And Crosswise Sutra; 2 Combined Operations Of Elementary Arithmetic; 3 Evaluation Of Determinants; 4 The Solution Of Simultaneous Linear Equations; 5 Inversion Of Matrices; 6 Curve-Fitting; 7 Evaluation Of Logarithms And Exponentials; 8 Change Of Roots Of Equations; 9 Sine, Cosine And Inverse Tangent; 10 Inverse Sine And Cosine And Tangent; 11 Transcendental Equations; 12 Solution Of Cubic And Higher Order Equations; 13 Functions Of Polynomials; 14 Functions Of Bipolynomials; 15 The Solution Of Linear And Non-Linear Differential, Integral And Integro-Differential Equations; 16 The Solution Of Linear And Non-Linear Partial Differential Equations.

$28.75

THE COSMIC COMPUTER COURSE, BOOK 3

By Kenneth R. Williams & Mark Gaskell

www.sacredscience.com Sacred Science Institute. 2006. Deluxe Hardcover Facsimile Edition Privately Printed. H Hard Cover Maroon Suede Guilt. New. 250p. This full course consists of the Textbook, the Teacher's Guide and the Answer Book. Book 3 develops this further into recurring decimals, square and cube roots, division, divisibility, the musical scale, formulae, simultaneous equations, quadratic equations, proof, similar triangles, area of a circle, nets, conic sections, loci, motion, vectors, Pythagoras' theorem, triples, coordinate geometry, Vedic Maths, etc.

$51.75