## Elements of Geometry: Containing the Principal Propositions in the First Six, and the Eleventh and Twelfth Books of Euclid. With Notes, Critical and ExplanatoryJohnson, 1803 - 279 pages |

### From inside the book

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... , WOOLWICH . THE THIRD EDITION . LONDON : PRINTED FOR J. JOHNSON , NO . 72 , ST . PAUL'S CHURCH - YARD , BY BYE AND LAW , ST , JOHN'S -

... , WOOLWICH . THE THIRD EDITION . LONDON : PRINTED FOR J. JOHNSON , NO . 72 , ST . PAUL'S CHURCH - YARD , BY BYE AND LAW , ST , JOHN'S -

**SQUARE**, CLERKENWELL . BOD 2 1 OCT 1965 LIBRARY PREFACE . OF all 1803 . ELEMENTS. Page 50

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**square**of a lefs ; and the greater**square**has the greater fide . Let the right line AB be greater than the right line EF ; then will BD , the**square**of AB , be greater than FH , the fquare of EF . For fince AB is greater than EF , and ... Page 57

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**square**of AB be equal to the fquares of AC , CB together with twice the rectangle of AC , CB . For upon AB make the**square**AD ( II . 1. ) , and draw the diagonal EB ; and make CK , FH parallel to AE , ED ( I. 27. ) Then , Then , fince ... Page 59

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**square**of AC . For , upon AB make the fquare AD ( II . 1. ) , and draw the diagonal BE ; and make FC , HK parallel to BD , BA- ( I. 27. ) : Then because AG is equal to GD ( II . 6. ) , to each of these equals add CK , and the whole AK ... Page 62

... together . Q. E. D. COROLL . The difference of the fquares of the hypo- tenuse and either of the other fides is equal to the

... together . Q. E. D. COROLL . The difference of the fquares of the hypo- tenuse and either of the other fides is equal to the

**square**of the remaining fide . PRO P. XV . THEOREM . If the fquare of PROP . 62 ELEMENTS OF GEOMETRY .### Contents

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### Other editions - View all

Elements of Geometry: Containing the Principal Propositions in the First Six ... Euclid,John Bonnycastle No preview available - 2016 |

### Common terms and phrases

ABCD AC is equal alfo equal alſo be equal alſo be greater altitude angle ABC angle ACB angle BAD angle CAB bafe baſe becauſe bifect cafe centre chord circle ABC circumference confequently Conft COROLL DABC defcribe demonftration diagonal diameter diſtance draw EFGH equiangular equimultiples EUCLID fame manner fame multiple fame plane fame ratio fecond fection fegment fhewn fide AB fide AC fimilar fince the angles firſt folid fome fquares of AC given circle given right line infcribe interfect join the points lefs leſs Let ABC magnitudes muſt oppofite angles outward angle parallelogram perpendicular polygon prifm propofition proportional Q. E. D. PROP reaſon rectangle of AB rectangle of AE remaining angle right angles ſame SCHOLIUM ſhewn ſpace ſquare tangent THEOREM theſe triangle ABC twice the rectangle uſeful whence

### Popular passages

Page 164 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Page 71 - The radius of a circle is a right line drawn from the centre to the circumference.

Page 69 - Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.

Page 205 - Lemma, if from the greater of two unequal magnitudes there be taken more than its half, and from the remainder more than its half, and so on, there shall at length remain a magnitude less than the least of the proposed magnitudes.

Page 18 - To draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it. LET ab be the given straight line, which may be produced to any length both ways, and let c be a point without it. It is required to draw a straight line perpendicular to ab from the point c.

Page 239 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.

Page 5 - AXIOM is a self-evident truth ; such as, — 1. Things which are equal to the same thing, are equal to each other. 2. If equals be added to equals, the sums will be equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals be added to unequals, the sums will be unequal. 5. If equals be taken from unequals, the remainders will be unequal.

Page 133 - If any number of magnitudes be equimultiples of as many others, each of each, what multiple soever any one of the first is of its part, the same multiple is the sum of all the first of the sum of all the rest.

Page 143 - F is greater than E; and if equal, equal; and if less, less. But F is any multiple whatever of C, and D and E are any equimultiples whatever of A and B; [Construction.

Page 155 - Of four proportional quantities, the first and third are called the antecedents, and the second and fourth the consequents ; and the last is said to be a fourth proportional to the other three taken in order.