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 TrigonometryW.E. Dean, 1839 - 318 páginas |
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Página 67
... Similar segments of a circle , are those in which the an- gles are equal , or which contain equal angles . PROP . I. PROB . е To find the centre of a given circle . Let ABC be the given circle ; it is required to find its centre . Draw ...
... Similar segments of a circle , are those in which the an- gles are equal , or which contain equal angles . PROP . I. PROB . е To find the centre of a given circle . Let ABC be the given circle ; it is required to find its centre . Draw ...
Página 81
... similar segments of circles , not 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 ...
... similar segments of circles , not 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 ...
Página 82
... similar to the segment ADB , and símilar segments of circles contain ( 9. def . 3. ) equal angles , the angle ACB is ... similar segments of circles upon the same side of the same line , which do not coincide . Q. E. D. PROP . XXIV ...
... similar to the segment ADB , and símilar segments of circles contain ( 9. def . 3. ) equal angles , the angle ACB is ... similar segments of circles upon the same side of the same line , which do not coincide . Q. E. D. PROP . XXIV ...
Página 84
... similar ( 9. def 3. ) to the segment EDF ; and they are upon equal straight lines BC , EF ; but similar segments of circles upon equal straight lines are equal ( 24. 3. ) to one another , therefore the segment BAC is equal to the ...
... similar ( 9. def 3. ) to the segment EDF ; and they are upon equal straight lines BC , EF ; but similar segments of circles upon equal straight lines are equal ( 24. 3. ) to one another , therefore the segment BAC is equal to the ...
Página 123
... . 5. ) , A : CDF . In the same manner may the proposition be demonstrat- ed , whatever be the number of ratios . Therefore , & c . Q. E. D. ELEMENTS OF GEOMETR Y. BOOK VI . DEFINITIONS . SIMILAR OF GEOMETRY . BOOK V. 123.
... . 5. ) , A : CDF . In the same manner may the proposition be demonstrat- ed , whatever be the number of ratios . Therefore , & c . Q. E. D. ELEMENTS OF GEOMETR Y. BOOK VI . DEFINITIONS . SIMILAR OF GEOMETRY . BOOK V. 123.
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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 opposite angle parallel parallelogram parallelopipeds perpendicular polygon prism PROB produced proportional 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 parallelopipeds spherical angle spherical triangle square straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore