Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids: to which are Added, Edlemnts of Plane and Spherical TrigonometryW.E. Dean, 1836 - 311 páginas |
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Página 313
... hypotenuse . From the centre C , with any ra- dius CD , describe the arch DE ; draw DF at right angles to CE , and from E draw EG touching the circle in E , and meeting CB in G ; DF is the sine , and EG the tangent of the arch DE , or ...
... hypotenuse . From the centre C , with any ra- dius CD , describe the arch DE ; draw DF at right angles to CE , and from E draw EG touching the circle in E , and meeting CB in G ; DF is the sine , and EG the tangent of the arch DE , or ...
Página 314
... hypotenuse . For CG is the secant of the angle C ( def . 7. ) , and the tri- angles CGE , CBA being equiangular , CA : CB :: CE CG , that is , CA : CB :: R : sec . C. COR . 2. If the analogies in this proposition , and in the above ...
... hypotenuse . For CG is the secant of the angle C ( def . 7. ) , and the tri- angles CGE , CBA being equiangular , CA : CB :: CE CG , that is , CA : CB :: R : sec . C. COR . 2. If the analogies in this proposition , and in the above ...
Página 315
... hypotenuse the secant of it . 91 dan Los que enz . The sides of a plane triangle are to one another as the sines of the opposite angles . { M From A any angle in the triangle ABC , let AD be drawn perpendicular to BC . And because the ...
... hypotenuse the secant of it . 91 dan Los que enz . The sides of a plane triangle are to one another as the sines of the opposite angles . { M From A any angle in the triangle ABC , let AD be drawn perpendicular to BC . And because the ...
Página 327
... hypotenuse and an angle . AC . AB . R : sin B :: CB : AC . 1 R : cos B :: CB : AB . 2 IR AC and C , a BC . side , and one of AB . Cos C : R :: AC : BC . R : tan C :: AC : AB . 34 the acute angles . CB and BA , the hypotenuse and a side ...
... hypotenuse and an angle . AC . AB . R : sin B :: CB : AC . 1 R : cos B :: CB : AB . 2 IR AC and C , a BC . side , and one of AB . Cos C : R :: AC : BC . R : tan C :: AC : AB . 34 the acute angles . CB and BA , the hypotenuse and a side ...
Página 328
... hypotenuse BC , a solution may also be obtained by help of the secant , for CA : CB :: R : sec . C ; if , there- fore , this proportion be made , R : sec . C :: AC :: CB , CB will be found , In the third case , when the hypotenuse BC ...
... hypotenuse BC , a solution may also be obtained by help of the secant , for CA : CB :: R : sec . C ; if , there- fore , this proportion be made , R : sec . C :: AC :: CB , CB will be found , In the third case , when the hypotenuse BC ...
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Términos y frases comunes
ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder definition demonstrated described diameter draw drawn equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism proportional proposition pyramid Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle spherical angle spherical triangle Spherical Trigonometry straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore
Pasajes populares
Página 58 - 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 26 - If two triangles have two sides of the one equal to two sides of the...
Página 46 - Wherefore, if a straight line, &c. QED PROP. XXIX. THEOR. s«e N. Ij'a straight line fall upon two parallel straight lines, it makes the alternate angles equal...
Página 74 - THEOR. //' a straight line be divided into two equal, and also into two unequal parts, the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section.
Página 84 - An angle in a segment is the angle contained by two straight lines drawn from any point in the circumference of the segment to the extremities of the straight . line which is the base of the segment.
Página 411 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.
Página 112 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Página 118 - 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 54 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Página 49 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are equal to two right angles.