## Euclid's Elements of Geometry, Books 1-6Henry Martyn Taylor The University Press, 1893 - 504 pages |

### From inside the book

Results 1-5 of 88

Page iv

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**proofs**of propo- sitions as given in Euclid will not be required , but no**proof**of any proposition occurring in Euclid will be admitted in which use is made of any proposition which in Euclid's order occurs subsequently . ' And in the ... Page viii

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**proofs**of the Propositions . The method is used directly by Euclid in his**proof**of Proposition 4 of Book I. , and indirectly in his**proofs**of Proposition 5 and of every other Proposition , in which the theorem of Proposition 4 is quoted ... Page ix

Henry Martyn Taylor.

Henry Martyn Taylor.

**proofs**of any theorems , in the**proofs**of which , in Euclid's text , the theorem of Proposition ...**proof**have been adopted in many cases . The chief instances of alteration are to be found in Propositions 5 and 6 of ... Page xi

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**proofs**of several of the Propositions have been given , which may be developed more fully and used in examinations , in place of the**proofs**given in the text . Some of these**proofs**are not , so far as I know , to be found in English ... Page 20

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**PROOF**. Because A is the centre of the circle EFG , AE is equal to AF . ( Def . 22. ) But AE was made equal to CD ; ( Construction . ) therefore AF is equal to CD . Wherefore , from AB the greater of two given straight lines a part AF ...### Other editions - View all

### Common terms and phrases

ABCD AC is equal ADDITIONAL PROPOSITION angle ACB angle BAC angles ABC anharmonic arc ABC bisected centre of similitude chord circle ABC coincide Constr Coroll cut the circle describe a circle diagonal diameter draw equal angles equal circles equal to CD equiangular equimultiples Euclid EXERCISES exterior angle given circle given point given straight line given triangle greater harmonic range hypotenuse inscribed intersect Let ABC meet middle points opposite sides pair parallel parallelogram pencil pentagon perpendicular polygon PROOF Prop PROPOSITION 14 Ptolemy's Theorem quadrilateral radical axis radius rectangle contained required to prove respectively rhombus right angles shew sides BC Similarly square on AC straight line &c straight line drawn straight line joining subtend tangent theorem triangle ABC triangle DEF triangles are equal twice the rectangle vertices Wherefore

### Popular passages

Page 59 - Any two sides of a triangle are together greater than the third side.

Page 7 - An angle less than a right angle is called an acute angle; an angle greater than a right angle and less than two right angles is called an obtuse angle.

Page 68 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.

Page 144 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced...

Page 376 - To find a mean proportional between two given straight lines. Let AB, BC be the two given straight lines ; it is required to find a mean proportional between them. Place AB, BC in a straight line, and upon AC describe the semicircle ADC, and from the point B draw (9.

Page 135 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.

Page 76 - ... the same side together equal to two right angles ; the two straight lines shall be parallel to one another.

Page 305 - To inscribe, an equilateral and equiangular pentagon in a given circle. Let ABCDE be the given circle. It is required to inscribe an equilateral...

Page 424 - PROPOSITION 5. The locus of a point, the ratio of whose distances from two given points is constant, is a circle*.

Page 248 - If two straight lines within a circle cut one another, the rectangle contained by the segments of one of them is equal to the rectangle contained by the segments of the other. Let the two straight lines AC, BD, within the circle ABCD, cut one another in the point E : the rectangle contained by AE, EC is equal to the rectangle contained by BE, ED.