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 σελίδες |
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Σελίδα ix
... less . In the same manner , the quadrature of the circle is performed only by approximation , or by finding two rectangles nearly equal to one another , one of them greater , and another less than the space contained within the circle ...
... less . In the same manner , the quadrature of the circle is performed only by approximation , or by finding two rectangles nearly equal to one another , one of them greater , and another less than the space contained within the circle ...
Σελίδα x
... less rigorous than that of the Greek Geometer ; for this would be to pay too dear even for the time that might thereby be saved : but it is done chiefly by laying aside a certain rule , which , though it be not essential to the accuracy ...
... less rigorous than that of the Greek Geometer ; for this would be to pay too dear even for the time that might thereby be saved : but it is done chiefly by laying aside a certain rule , which , though it be not essential to the accuracy ...
Σελίδα 23
... less . Let AB and C be the two given straight lines , whereof AB is the greater . It is required to cut off D from AB , the greater , a part equal to C , the less . From the point A draw ( 2. 1. ) the straight line AD equal to C ; and ...
... less . Let AB and C be the two given straight lines , whereof AB is the greater . It is required to cut off D from AB , the greater , a part equal to C , the less . From the point A draw ( 2. 1. ) the straight line AD equal to C ; and ...
Σελίδα 25
... less , and join DC ; therefore , be- cause in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; but the angle DBC is also equal to the angle ACB ...
... less , and join DC ; therefore , be- cause in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; but the angle DBC is also equal to the angle ACB ...
Σελίδα 30
... less to the greater , which is impossible ; therefore BE is not in the same straight line with BC . And in like manner , it may be demonstrated , that no other can be in the same straight line with it but BD , which therefore is in the ...
... less to the greater , which is impossible ; therefore BE is not in the same straight line with BC . And in like manner , it may be demonstrated , that no other can be in the same straight line with it but BD , which therefore is in the ...
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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 MDCCCXX 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