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, 1851 - 317 σελίδες |
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Σελίδα 88
... consequently the two circles cannot cut each other . PROP . D. THEOR . In the same circle , equal angles at the centre are subtended by equal arcs ; and , conversely , equal arcs subtend equal angles at the centre . Let C be the centre ...
... consequently the two circles cannot cut each other . PROP . D. THEOR . In the same circle , equal angles at the centre are subtended by equal arcs ; and , conversely , equal arcs subtend equal angles at the centre . Let C be the centre ...
Σελίδα 92
... consequently the circle which passes through the three points A , B , C , will also pass through the point D. By the ... consequently , being chords of the circumscribed circle , they are equal , and therefore include equal angles ...
... consequently the circle which passes through the three points A , B , C , will also pass through the point D. By the ... consequently , being chords of the circumscribed circle , they are equal , and therefore include equal angles ...
Σελίδα 99
... consequently the three angles BDA , DBA , BCD , are equal to one another . And because the angle DBC is equal to the angle BCD , the side BD is equal ( 6. 1. ) to the side DC ; but BD was made equal to CA ; therefore also CA is equal to ...
... consequently the three angles BDA , DBA , BCD , are equal to one another . And because the angle DBC is equal to the angle BCD , the side BD is equal ( 6. 1. ) to the side DC ; but BD was made equal to CA ; therefore also CA is equal to ...
Σελίδα 118
... consequently D7F ( 10. 5. ) . Next , let A = C ; then A : B :: C : B ( 7. 5. ) , but A : B :: D : E ; there- fore , C : B :: D : E , but C : B :: F : E , therefore , D : E :: F : E ( 11 . 5. ) , and D F ( 9. 5. ) . Lastly , let A / C ...
... consequently D7F ( 10. 5. ) . Next , let A = C ; then A : B :: C : B ( 7. 5. ) , but A : B :: D : E ; there- fore , C : B :: D : E , but C : B :: F : E , therefore , D : E :: F : E ( 11 . 5. ) , and D F ( 9. 5. ) . Lastly , let A / C ...
Σελίδα 120
... consequently A and B together must be equal to 14 times C , so that C measures the sum of A and B ; likewise , since the difference of A and B is equal to 4 times C , C also measures this difference . And had any other numbers been ...
... consequently A and B together must be equal to 14 times C , so that C measures the sum of A and B ; likewise , since the difference of A and B is equal to 4 times C , C also measures this difference . And had any other numbers been ...
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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated described diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROB PROP proportional proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR touches the circle triangle ABC triangle DEF wherefore