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### Innhold

 Historical Sketch 7 BOOK II 15 Ratio and Proportion 40 BOOK III 51 Comparison and Measurement of Polygons 66 BOOK 93 Regular Polygons and the Area of the Circle 110 Exercises on the preceding Books 125
 Nature and Use of Logarithms 271 Multiplication Division etc by Logarithms 278 Solution of Rightangled Triangles 287 Solution of Obliqueangled Triangles 293 Instruments used in Drawing 299 Values of the Sines Cosines etc of certain Angles 305 306 Logarithms of Numbers from 1 to 10000 321 Logarithmic Sines and Tangents for every Minute of the Quadrant 343

 Planes and Solid Angles 137 Polyedrons 152 Spherical Triangles and Spherical Polygons 174 Measurement of the Three Round Bodies 191 Exercises on the preceding Principles 201 201 Exercises on the Parabola 217 The Hyperbola 240 Exercises on the Hyperbola 262
 APPENDIX 389 Miscellaneous Propositions 391 Tangents treated by the Method of Limits 402 Symmetrical Figures 408 Transversals 417 Poles and Polars with Respect to an Angle 424 Centres of Similitude 430 Perspective or Conical Projection 436

### Populĉre avsnitt

Side 35 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Side 187 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Side 20 - Wherefore, when a straight line, &c. QED PROP. XIV. THEOR. If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Side 124 - The area of a circle is equal to the product of its circumference by half the radius.* Let ACDE be a circle whose centre is O and radius OA : then will area OA— ^OAxcirc.
Side 23 - BC common to the two triangles, which is adjacent to their equal angles ; therefore their other sides shall be equal, each to each, and the third angle of the one to the third angle of the other, (26.
Side 64 - BEC, taken together, are measured by half the circumference ; hence their sum is equal to two right angles.
Side 177 - THEOREM. The sum of the sides of a spherical polygon, is less than the circumference of a great circle. Let...
Side 31 - BAC equal to the third angle EDF. For if BC be not equal to EF, one of them must be greater than the other. Let BC be the greater, and make BH equal to EF, [I.
Side 73 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Side 73 - The rectangle contained by the sum and difference of two lines, is equivalent to the difference of the squares of those lines.