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 Elements of Plane and Spherical TrigonometryE. Duyckinck, and George Long, 1824 - 333 σελίδες |
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Σελίδα 81
... coinciding with one another . If it be possible , let the two similar segments of circles , viz . ACB , ADB , be upon the same side of the same straight line AB , not coin- ciding with one another ; then , because the circles ACB , ADB ...
... coinciding with one another . If it be possible , let the two similar segments of circles , viz . ACB , ADB , be upon the same side of the same straight line AB , not coin- ciding with one another ; then , because the circles ACB , ADB ...
Σελίδα 82
... coincide . Q. E. D. PROP . XXIV . THEOR . Similar segments of circles upon equal straight lines are equal to one ... coincide with the point D , because AB is equal to CD : A BC D Therefore the straight line AB coinciding with CD , the ...
... coincide . Q. E. D. PROP . XXIV . THEOR . Similar segments of circles upon equal straight lines are equal to one ... coincide with the point D , because AB is equal to CD : A BC D Therefore the straight line AB coinciding with CD , the ...
Σελίδα 197
... coincide ( 8. Ax . 1. ) , the point N coinciding with the point D , K with A , L with B , and so on . And because the plane KM coincides with the plane AC , and , by hy- pothesis , the inclination of KR to KM is the same with the ...
... coincide ( 8. Ax . 1. ) , the point N coinciding with the point D , K with A , L with B , and so on . And because the plane KM coincides with the plane AC , and , by hy- pothesis , the inclination of KR to KM is the same with the ...
Σελίδα 213
... coincides with EG , the two rectangles AH and EH will coin- cide , and the straight line AD will coincide with the straight line EF . But AD is always in the superficies of the cylinder , for it describes that superficies ; therefore ...
... coincides with EG , the two rectangles AH and EH will coin- cide , and the straight line AD will coincide with the straight line EF . But AD is always in the superficies of the cylinder , for it describes that superficies ; therefore ...
Σελίδα 241
... coincide with A , R : cos . BC : sin . BC : sin . BD , that is the radius is to the cosine of any arch , as the sine of the arch is to half the sine of twice the arch ; or if any arch = A , sin . 2A = sin . A Xcos . A , or sin . 2A = 2 ...
... coincide with A , R : cos . BC : sin . BC : sin . BD , that is the radius is to the cosine of any arch , as the sine of the arch is to half the sine of twice the arch ; or if any arch = A , sin . 2A = sin . A Xcos . A , or sin . 2A = 2 ...
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ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder demonstrated diameter draw 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 multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore