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 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 . 1. PROB . 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 . 1. PROB . 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 similar segments of circles con- tain ( 9. def . 3. ) equal angles , the angle ACB is equal to the angle ADB , the exte- A rior to the interior , which is impossible ( 16. 1. ) . Therefore , there cannot ...
... similar to the segment ADB , and similar segments of circles con- tain ( 9. def . 3. ) equal angles , the angle ACB is equal to the angle ADB , the exte- A rior to the interior , which is impossible ( 16. 1. ) . Therefore , there cannot ...
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 132
... similar to the whole triangle , and to one another . Let ABC be a right angled triangle , having the right angle BAC ; and from the point A let AD be drawn perpendicular to the base BC the triangles ABD , ADC are similar to the whole ...
... similar to the whole triangle , and to one another . Let ABC be a right angled triangle , having the right angle BAC ; and from the point A let AD be drawn perpendicular to the base BC the triangles ABD , ADC are similar to the whole ...
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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 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