The synoptical Euclid; being the first four books of Euclid's Elements of geometry, with exercises, by S.A. Good1853 |
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Página 78
... equal ( III . Def . 4. ) ; therefore 10. AB , CD , are equally distant from the centre E. Next , if the straight ... AF , and CD double of CG , 2 . EG , GC ; The squares of EF , FA , are equal to the squares of of which the square of FE ...
... equal ( III . Def . 4. ) ; therefore 10. AB , CD , are equally distant from the centre E. Next , if the straight ... AF , and CD double of CG , 2 . EG , GC ; The squares of EF , FA , are equal to the squares of of which the square of FE ...
Página 84
... the same reason , 2. The angle BFD is double of the angle BED : therefore ( Ax . 7. ) 3. The angle BAD is equal to the angle BED . Next , let the segment BAED be not greater than a semicircle . B A E F Draw AF to the centre , and ...
... the same reason , 2. The angle BFD is double of the angle BED : therefore ( Ax . 7. ) 3. The angle BAD is equal to the angle BED . Next , let the segment BAED be not greater than a semicircle . B A E F Draw AF to the centre , and ...
Página 94
... equal to the angle C. First , let the angle C be a right angle . H град A B Bisect ( I. 10. ) AB in F , and from the ... AF is equal to FB , and FG common to the triangles AFG , BFG , the two sides AF , FG , are equal to the two BF , FG ...
... equal to the angle C. First , let the angle C be a right angle . H град A B Bisect ( I. 10. ) AB in F , and from the ... AF is equal to FB , and FG common to the triangles AFG , BFG , the two sides AF , FG , are equal to the two BF , FG ...
Página 96
... F , F is the centre of the circle ABCD . Join AF . And because BD , which passes through the centre , cuts the straight line AC , which does not pass through the centre , at right angles in E , ( III . 3. ) 1. AE , EC , are equal to one ...
... F , F is the centre of the circle ABCD . Join AF . And because BD , which passes through the centre , cuts the straight line AC , which does not pass through the centre , at right angles in E , ( III . 3. ) 1. AE , EC , are equal to one ...
Página 97
... equal to the squares of AG , GF ; but the squares of EG , GF , are equal ( I. 47. ) to the square of EF ; and the squares of AG , GF , are equal to the square of AF ; therefore 4. The rectangle AE , EC , together with the square of EF , is ...
... equal to the squares of AG , GF ; but the squares of EG , GF , are equal ( I. 47. ) to the square of EF ; and the squares of AG , GF , are equal to the square of AF ; therefore 4. The rectangle AE , EC , together with the square of EF , is ...
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Términos y frases comunes
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
Pasajes populares
Página 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...
Página 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.
Página 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.
Página 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.
Página 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.
Página 7 - AB; but things which are equal to the same are equal to one another...
Página 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.
Página 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.
Página 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.
Página 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...