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

### From inside the book

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**hypotenuse**of a right - angled triangle is greater than either of the other sides . 2. The base of a triangle is divided into two parts by the perpen- dicular from the opposite vertex : prove that each part of the base is less than the ... Page 61

... Construct a right - angled triangle , having given the

... Construct a right - angled triangle , having given the

**hypotenuse**and one side . 4. Construct a quadrilateral equal in all respects to a given quadrilateral . PROPOSITION 23 . From a given point in a given PROPOSITION 22 . 61. Page 71

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**hypotenuse**IA is common , and IN is equal to IM , the triangles are equal in all respects : ( Exercise 5 , page 49. ) therefore the angle IAN is equal to the angle IAM , and IA is the bisector of the angle BAC . Therefore the bisector ... Page 73

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**hypotenuse**and a side of the one be respectively equal to the**hypotenuse**and a side of the other . 4. If two exterior angles of a triangle be bisected , and from the point of intersection of the bisecting lines a straight line be drawn ... Page 87

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**hypotenuse**is equal to half the**hypotenuse**. 8. The locus of the vertices of all right - angled triangles which have a common**hypotenuse**is a circle . PROPOSITION 33 . If two sides of a convex quadrilateral PROPOSITION 32 . 87.### 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.