The elements of geometry: in which the principal propositions of Euclid, Archimedes, and others are demonstrated after the most easy manner. To which is added, a collection of useful geometrical problems. Also, the Doctrine of proportion, arithmetical and geometrical, together with a general method of arguing by proportional quantities (Google eBook)

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F. Wingrave, 1794 - Geometry - 216 pages
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Page 204 - ... the remaining ratio of the last. LET the first ratios be those of a to' b, b to С, С to d, d to e, and e to f ; and let the other ratios be those of g to h, h to k, k to l, and l to m ; also, let the ratio of a to f, which is compounded of (def.
Page 185 - If equal quantities be added to equal quantities, the sums will be equal.
Page 49 - Straight lines are said to be ' equally distant from the centre ' of a circle, when the perpendiculars drawn to them from the centre are equal.
Page 25 - As the (quart of the hyporhcnufc, or longed fide of a right-angled triangle, is equal to the fum of the fquares of the other two fides...
Page 88 - MN. 3. // a line is perpendicular to one of two parallel planes, it is perpendicular to the other plane also.
Page 48 - ... SECTION IV. Of the Circle, and Inscribed and Circum scribed Figures. Definitions. 1. A circle is a plane figure described by a right line moving about a fixed point, as A A c about c : or it is a figure bounded by one line equidistant from a fixed point. 2. The centre of a circle is the fixed point about which the line moves, c. 3. The radius is the line that describes the circle, c A. Cor. All the radii of a circle are equal. 4. The circumference is the line described by the extreme end...
Page 92 - BG: for the same reason, in the triangles KAL, MBN, KL is equal to MN, and AL to BN : and in the triangles LAD, NBG, LA, AD are equal to NB, BG, and they contain equal angles ; therefore the base LD is equal (4.
Page 30 - Three lines drawn from the three angles of a triangle to the middle of the opposite sides, all meet in one point.
Page 111 - Becaufe every cone is the third part of a cylinder of the fame bafe and altitude, Multiply the area of its bafe by one third part of its height ; the product is the foiidity.
Page 8 - IEF=(FED)=AEF (by part 2. theo. 3.) a greater to a less, which is absurd, whence IK is not parallel ; and the like we can prove of all other lines but AB ; therefore AB is parallel to CD. QED THEO. XII.

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