## The synoptical Euclid; being the first four books of Euclid's Elements of geometry, with exercises, by S.A. Good1853 |

### From inside the book

Results 1-5 of 13

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**angle EDF**: the base BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite , shall be equal , each to each , viz . the angle ABC to the angle DEF ... Page 13

... angle BAC coincides with the

... angle BAC coincides with the

**angle EDF**, and is equal ( Ax . 8. ) to it . Therefore if two triangles , & c . Q.E.D. PROP . IX . - PROBLEM . To bisect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be ... Page 25

... the base CB greater than the base EF ; the angle BAC is likewise greater than the

... the base CB greater than the base EF ; the angle BAC is likewise greater than the

**angle EDF**. D For if it be not greater , it must either B 2 E BOOK I. - PROP . XXIV . XXV . 25 DF; but the angle BAC greater than the angle ... Page 26

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**angle EDF**, because then the base BC would be equal ( I. 4. ) to EF ; but it is not , therefore 1. The angle BAC is not equal to the**angle EDF**. Neither is it less ; because then the base BC would be less ( I. 24. ) than the base EF ... Page 27

... angle ABC is equal ( Hyp . ) to the angle DEF ; therefore ( I. 4. ) 7. The base AC is equal to the base DF , and the third angle BAC to the third

... angle ABC is equal ( Hyp . ) to the angle DEF ; therefore ( I. 4. ) 7. The base AC is equal to the base DF , and the third angle BAC to the third

**angle EDF**. Next , let the sides which are opposite to equal angles in each triangle be ...### Other editions - View all

### Common terms and phrases

ABC is equal adjacent angles AF is equal angle ABC angle ACB angle AGH angle BAC angle BCD angle DEF angle EAB angle EDF angle equal base BC bisected circle ABC cuts the circle describe a circle diameter double equal angles equal Constr equal Hyp equal straight lines equal to BC equiangular equilateral and equiangular EUCLID'S ELEMENTS exterior angle given circle given rectilineal angle given straight line given triangle gnomon greater inscribed join Let ABC Let the straight likewise opposite angles parallel to CD parallelogram pentagon perpendicular point F Q.E.D. PROP rectangle AD rectangle AE rectangle contained rectilineal figure remaining angle required to describe right angles semicircle side BC square of AC straight line AB straight line AC touches the circle triangle ABC triangle DEF twice the rectangle

### Popular passages

Page 26 - 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. either the sides adjacent to the equal...

Page 22 - If from the ends of a side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle.

Page 32 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Page 1 - A plane superficies is that in which any two points being taken, the straight line between them lies wholly in that superficies. vm. "A plane angle is the inclination of two lines to one another in a plane, which meet together, but are not in the same direction.

Page 97 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.

Page 7 - AB; but things which are equal to the same are equal to one another...

Page 14 - To bisect a given finite straight line, that is, to divide it into two equal parts. Let AB be the given straight line : it is required to divide it intotwo equal parts.

Page 53 - IF a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part.

Page 41 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.

Page 52 - 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...