## Appendix to the Mensuration: For the Use of Teachers |

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### Common terms and phrases

A B D F abscissa angle arithmetical progression base bisects centre circle circumference circumscribed cylinder circumscribed sphere conjugate diameters conoid curve distance divided ellipse F cº found by multiplying frustum greatest term half the conjugate half the transverse height hence hyperbola infinite number inscribed sphere latus rectum length mean proportional number of terms oblate spheroid ordinate parabola parallel perpendicular polygon prolate spheroid Prop PROPOSITION radius rectangle rule sector segment similar triangles solidity square of half surface tabular number tangent transverse and conjugate transverse axis trapezium versed sine vertex

### Popular passages

Page 67 - The area of a circle is equal to the area of a triangle, whose base is equal to the circumference and perpendicular equal to the radius.

Page 35 - If one angle at the base of a triangle be double of the other, the less side is equal to the sum or difference of the segments of the base made by the perpendicular from the vertex, according as the angle is greater or less than a right angle.

Page 31 - ... side of the square DG along the ruler B c, and at the same time keep the thread continually tight by means of the pin M, with its part M o close to the side of the square D o ; so shall the curve AM x, which the pin describes by this motion, be one part of a parabola. And if the square be turned over, and moved on the other side of the fixed point F, the other part of the same parabola AM z will be described. 7. PROB. Any right line being given in a parabola, to find the corresponding diameter...

Page 43 - Indivisibles, which was published in 1635, he considered a line as composed of an infinite number of points, a surface of an infinite number of lines, and a solid of an infinite number of surfaces ; and he...

Page 58 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — b) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.

Page 108 - But the solidity of a cylinder is found by multiplying the area of its base by the height.

Page 84 - As the conjugate diameter is to the transverse, so is the square root of the difference of the squares of the ordinate and...

Page 4 - That part of the diameter between the vertex and the ordinate is called an abscissa ; thus GB, and AG, are abscissas to the ordinate G E.

Page 95 - ... can be divided into pyramids and parallelepipeds. But in intricate cases it is easier to use fluxions, and consider the solid generated by the motion of...

Page 99 - This rule may be easily deduced from the preceding ones. Other rules are given, which find the true solidity only when the middle section, between the two ends, is similar to the two ends ; which never can be except when the parallel ends are similar ellipses ; that is, the transverse and conjugate diameters at each end parallel to each other ; this can never happen but when the solid is the frustum of an elliptical cone.