# The Geometrician: Containing Essays on Plane Geometry, and Trigonometry: with Their Application to the Solutions of a Variety of Problems ...

J. Johnson, 1775 - Geometry, Plane - 159 pages
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Page 23 - The lines do not run in a uniform direction from the left to the right, or from the right to the left...
Page 102 - AB, remains the same as it was : Nor is it part of the length of the line AB ; for, if AB be removed from the line KB, the point B, which is the extremity of the line KB, does...
Page 115 - If a point be taken within a circle, from which there fall more than two equal straight lines to the circumference, that point is the centre of the circle. Let...
Page 9 - If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous sides.
Page 41 - ... magnitude. For example, if A, B, C, D be four magnitudes of the same kind, the first A is said to have to the last D the ratio compounded of the ratio of A to B, and of the ratio of B to C, and of the ratio of C to D; or, the ratio of A to D is said to be compounded of the ratios of A to B, B to C, and C to D. And if...
Page 101 - It is necessary to consider a solid, that is, a magnitude which has length, breadth, and thickness, in order to understand aright the definitions of a point, line and superficies ; for these all arise from a solid, and exist in it ; The boundary, or boundaries which contain a solid, are called superficies, or the boundary which is common to two solids which are contiguous, or which divides one solid into two contiguous parts, is called a superficies...
Page 41 - When three magnitudes are proportionals, the first is said to have to the third the duplicate ratio of that which it has to the second.
Page 58 - ... is supposed to be divided into 60 equal parts, called minutes; and each minute into 60 equal parts, called seconds. Degrees, minutes, and seconds, are designated respectively, by the characters � ' ". For example, ten degrees, eighteen minutes, and fourteen seconds, would be written 10� 18
Page 12 - If two triangles have two sides of the one equal to two sides of the...
Page 102 - KBCL which is contiguous to it, this boundary BC is called a line, and has no breadth : For if it have any, this...