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 Trigonometry |
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Page 56
... produced to any point ; the rectangle contained by the whole line thus produced , and the part of it produced , together with the square of half the line bisected , is equal to the square of the straight line which is made up of the ...
... produced to any point ; the rectangle contained by the whole line thus produced , and the part of it produced , together with the square of half the line bisected , is equal to the square of the straight line which is made up of the ...
Page 60
... produced to any point , the square of the whole line thus produced , and the square of the part of it produ- ced , are together double of the square of half the line bisected , and of the square of the line made up of the half and ...
... produced to any point , the square of the whole line thus produced , and the square of the part of it produ- ced , are together double of the square of half the line bisected , and of the square of the line made up of the half and ...
Page 62
... produced , the square of the side subtending the obtuse angle is greater than the squares of the sides con- taining the obtuse angle , by twice the rectangle contained by the side upon which , when produced , the perpendicular falls ...
... produced , the square of the side subtending the obtuse angle is greater than the squares of the sides con- taining the obtuse angle , by twice the rectangle contained by the side upon which , when produced , the perpendicular falls ...
Page 126
... produced , proportionally : And if the sides , or the sides produced , be cut proportionally , the straight line which joins the points of section will be parallel to the remaining side of the triangle . Let DE be drawn parallel to BC ...
... produced , proportionally : And if the sides , or the sides produced , be cut proportionally , the straight line which joins the points of section will be parallel to the remaining side of the triangle . Let DE be drawn parallel to BC ...
Page 128
... produced ; the segments between the bisecting line and the extremities of the base have the same ratio which the other sides of the triangles have to one another : And if the segments of the base produced have the same ratio which the ...
... produced ; the segments between the bisecting line and the extremities of the base have the same ratio which the other sides of the triangles have to one another : And if the segments of the base produced have the same ratio which the ...
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Common terms and phrases
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 BD THEOR third touches the circle triangle ABC triangle DEF wherefore