# A Treatise on Geometry and Its Application in the Arts

Longman, Orme, Brown, Green, & Longmans, 1840 - Curves, Plane - 314 pages
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### Popular passages

Page 84 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 44 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 124 - Four quantities are in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth.
Page 83 - Therefore all the interior angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 40 - EBF, there are two angles in the one equal to two angles in the other, each to each ; and the side EF, which is opposite to one of the equal angles in each, is common to both ; therefore the other sides are equal ; (i.
Page 40 - If one angle of a triangle be equal to the sum of the other two, the greatest side is double of the distance of its middle point from the opposite angle.
Page 169 - The volume of the frustum of any pyramid is equal to the sum of the volumes of three pyramids whose common altitude is the altitude of the frustum, and whose bases are the lower base, the upper base, and the mean proportional between the bases of the frustum.
Page 46 - Euclid's, and show by construction that its truth was known to us ; to demonstrate, for example, that the angles at the base of an isosceles triangle are equal...
Page 212 - ... solid is, as before, a solid inscribed in a larger sphere ; and, since the perpendicular on any side of the revolving polygon is equal to the radius of the inner sphere, the proposition is identical with Prop. 26. COR The solid circumscribed about the smaller sphere is greater than four times the cone whose base is a great circle of the sphere and whose height is equal to the radius of the sphere. For, since the surface of the solid is greater than four times the great circle of the inner sphere...
Page 40 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...