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 σελίδες |
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Σελίδα 19
... semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter . XV . Rectilineal figures are those which are contained by straight lines . XVI . Trilateral figures , or triangles , by three ...
... semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter . XV . Rectilineal figures are those which are contained by straight lines . XVI . Trilateral figures , or triangles , by three ...
Σελίδα 63
... semicircle BHF , and produce DE to H , and join GH . Therefore , because the straight line BF is divided into two equal parts in the point G , and into two unequal in the point E , the rectangle BE.EF , together with the square of EG ...
... semicircle BHF , and produce DE to H , and join GH . Therefore , because the straight line BF is divided into two equal parts in the point G , and into two unequal in the point E , the rectangle BE.EF , together with the square of EG ...
Σελίδα 80
... semicircle , and join BF , FD : And because the angle BFD is at the tre , and the angle BAD at the circumfer- ence , both having the same part of the cir - B cumference , viz . BCD , for their base ; therefore the angle BFD is double ...
... semicircle , and join BF , FD : And because the angle BFD is at the tre , and the angle BAD at the circumfer- ence , both having the same part of the cir - B cumference , viz . BCD , for their base ; therefore the angle BFD is double ...
Σελίδα 81
... semicircle , let BAD , BED be an- gles in it ; these also are equal to one ano- ther . Draw AF to the centre , and pro- duce to C , and join CE : Therefore the seg- ment BADC is greater than a semicircle ; and the angles in it BAC , BEC ...
... semicircle , let BAD , BED be an- gles in it ; these also are equal to one ano- ther . Draw AF to the centre , and pro- duce to C , and join CE : Therefore the seg- ment BADC is greater than a semicircle ; and the angles in it BAC , BEC ...
Σελίδα 82
... the segment ABC is a semicircle . Next let the angles ABD , BAD be unequal , at the point A , in the straight line AB make ( 23 . 1. ) the angle BAE equal to the angle ABD , and produce BD if neces- B B B E D A C A D C 82 ELEMENTS.
... the segment ABC is a semicircle . Next let the angles ABD , BAD be unequal , at the point A , in the straight line AB make ( 23 . 1. ) the angle BAE equal to the angle ABD , and produce BD if neces- B B B E D A C A D C 82 ELEMENTS.
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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 definition 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 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 straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore