## Manual of Geometry and Conic Sections: With Applications to Trigonometry and Mensuration |

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altitude axis base called centre chord circle circumference circumscribed coincide common cone consequently construct corresponding Cosine Cotang curve Definitions denoted diameter difference distance divide draw drawn edges equal EXAMPLES extremities faces fall formula four frustum given greater half hence included inscribed intersect lateral less Let ACD logarithm mean measured meet middle multiplied opposite parallel parallelogram pass perpendicular placed plane polygon position prism PROBLEM prolongation proportional PROPOSITION proved pyramid radii radius rectangle regular remaining revolved right angles RULE Scho segments shown sides similar Sine solution sphere spherical triangle square straight line subtracting suppose surface Tang tangent term THEOREM third triangle unit vertex volume whence

### Popular passages

Page 72 - In any proportion, the product of the means is equal to the product of the extremes.

Page 72 - If the product of two quantities is equal to the product of two others, two of them may be made the means, and the other two the extremes of a proportion. Let bc=ad.

Page 19 - A Polygon of three sides is called a triangle ; one of four sides, a quadrilateral; one of five sides, a pentagon; one of six sides, a hexagon; one of seven sides, a heptagon; one of eight sides, an octagon ; one of ten sides, a decagon ; one of twelve sides, a dodecagon, &c.

Page 273 - If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal in all their parts." Axiom 1. "Things which are equal to the same thing, are equal to each other.

Page 108 - 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 1 - O's, points or dots are introduced instead of the 0's through the rest of the line, to catch the eye, and to indicate that from thence the annexed first two figures of the Logarithm in the second column stand in the next lower line. N'.

Page 36 - The sum of the interior angles of a polygon is equal to twice as many right angles as the polygon has sides, less four right angles.

Page 104 - The sum of the squares of two sides of a triangle is equal to twice the square of half the third side increased by twice the square of the median upon that side.

Page 36 - ... therefore the sum of the angles of all the triangles is equal to twice as many right angles as the figure has sides. But the sum of all the angles...

Page 70 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D; and read, A is to B as C to D.