The geometry, by T. S. Davies. Conic sections, by Stephen FenwickJ. Weale, 1853 |
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Σελίδα 47
... Similar segments of a circle are those in which the angles are equal , or which contain equal angles . PROPOSITIONS . PROPOSITION I. PROB . To find the centre of a given circle . Let ABC be the given circle ; it is required to find its ...
... Similar segments of a circle are those in which the angles are equal , or which contain equal angles . PROPOSITIONS . PROPOSITION I. PROB . To find the centre of a given circle . Let ABC be the given circle ; it is required to find its ...
Σελίδα 60
... similar to the segment ADB , and that similar segments of circles contain ( 11 Def . III . ) equal angles ; the angle ACB is equal to the angle ADB , the exterior to the interior , which is impossible ( 16. 1. ) . Therefore , there ...
... similar to the segment ADB , and that similar segments of circles contain ( 11 Def . III . ) equal angles ; the angle ACB is equal to the angle ADB , the exterior to the interior , which is impossible ( 16. 1. ) . Therefore , there ...
Σελίδα 61
... similar segments , etc. PROPOSITION XXV . Q. E. D. PROB . A segment of a circle being given , to describe the circle of which it is the segment . Let ABC be the given segment of a circle : it is required to describe the circle of which ...
... similar segments , etc. PROPOSITION XXV . Q. E. D. PROB . A segment of a circle being given , to describe the circle of which it is the segment . Let ABC be the given segment of a circle : it is required to describe the circle of which ...
Σελίδα 62
... similar ( 11 Def . 111. ) to the segment EDF ; and they are upon equal straight lines BC , EF : B K E H But similar segments of circles upon equal straight lines are equal ( 24. 111. ) to one another ; therefore the segment BAC is equal ...
... similar ( 11 Def . 111. ) to the segment EDF ; and they are upon equal straight lines BC , EF : B K E H But similar segments of circles upon equal straight lines are equal ( 24. 111. ) to one another ; therefore the segment BAC is equal ...
Σελίδα 71
... similar to the greater and the less to the less ; and the diameters through the points of intersection of the line with the circles will be parallel . 14. Through two given points to describe a circle which shall bisect the ...
... similar to the greater and the less to the less ; and the diameters through the points of intersection of the line with the circles will be parallel . 14. Through two given points to describe a circle which shall bisect the ...
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ABC is equal ABCD adjacent angles angle ABC angle BAC axis bisected centre circle ABC circumference coincide cone construction coordinate planes described Descriptive Geometry diameter dicular dihedral angles draw edges ellipse equal angles equiangular equimultiples given line given point given straight line greater hence horizontal hyperbola inclination intersection join less Let ABC Let the plane line BC lines drawn magnitudes meet multiple orthograph parabola parallel planes parallelogram parallelopiped perpen perpendicular perpendicular to MN plane MN plane of projection plane parallel plane PQ prisms profile angles profile plane projecting plane Prop Q. E. D. PROPOSITION ratio rectangle rectangle contained rectilineal figure remaining angle respectively right angles SCHOLIUM segment sides six right sphere spherical angle tangent THEOR trace triangle ABC trihedral vertex Whence Wherefore