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 91
... bisect it . Join AB , and bisect it ( I. 10. ) in C ; from the point C draw ( I. 11. ) CD at right angles to AB ; the circumference ADB is bisected in the point D. A C B Join AD , DB . And because AC is equal to CB , and CD common to ...
... bisect it . Join AB , and bisect it ( I. 10. ) in C ; from the point C draw ( I. 11. ) CD at right angles to AB ; the circumference ADB is bisected in the point D. A C B Join AD , DB . And because AC is equal to CB , and CD common to ...
Página 94
... Bisect ( I. 10. ) AB in F , and from the centre F , at the distance FB , describe the semicircle AHB ; therefore ( III . 31. ) at C. The angle AHB in the semicircle is equal to the right angle But if the angle C be not a right angle ...
... Bisect ( I. 10. ) AB in F , and from the centre F , at the distance FB , describe the semicircle AHB ; therefore ( III . 31. ) at C. The angle AHB in the semicircle is equal to the right angle But if the angle C be not a right angle ...
Página 96
... bisected in 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 ...
... bisected in 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 ...
Página 98
... bisect it ( III . 3. ) ; therefore 1. AF is equal to FC : and because the straight line AC is bisected in F , and produced to D , ( II . 6. ) 2 . The rectangle AD , DC , together with the square of FC , is equal to the square of FD : to ...
... bisect it ( III . 3. ) ; therefore 1. AF is equal to FC : and because the straight line AC is bisected in F , and produced to D , ( II . 6. ) 2 . The rectangle AD , DC , together with the square of FC , is equal to the square of FD : to ...
Página 104
... Bisect ( I. 9. ) the angles ABC , BCA , by the straight lines BD , CD , meeting one another in the point D , from which draw ( I. 12. ) DE , DF , DG , perpendiculars to AB , BC , CA. E B And because the angle EBD is equal to the angle ...
... Bisect ( I. 9. ) the angles ABC , BCA , by the straight lines BD , CD , meeting one another in the point D , from which draw ( I. 12. ) DE , DF , DG , perpendiculars to AB , BC , CA. E B And because the angle EBD is equal to the angle ...
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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...