 | John Playfair - Geometry - 1829 - 210 pages
...duplicate ratio of that which their homologous sides have to each other. ED. PROPOSITION XXIII. THEOREM. Equiangular parallelograms have to one another the...ratio which is compounded of the ratios of their sides about the equal angles ; " that is, they are to one another as the rectangles contained by the sides... | |
 | John Martin Frederick Wright - Astronomy - 1831 - 282 pages
...axis intercepted between the origin and the normal. TRINITY COLLEGE, 1829. 1 . EQUIANGULAR / — 73 have to one another the ratio which is compounded of the ratios of their sides. 2. If two straight lines be J_ to the same plane, they are || to one another. 3. Required the value... | |
 | Industrial arts - 1831 - 532 pages
...and join AB and DE. The parallelograms CF and CO are evidently equiangular ; they have, therefore, to one another the ratio which is compounded of the ratios of their sides (23 of VI); that is, the ratio which is IMPROVED MODE OF PRESERVING BEBH FROM SOCRINC. of the ratios... | |
 | Euclides - 1834 - 518 pages
...ratios that are the same with the ratios of the sides. And to this demonstration agrees the enunciation have to one another the ratio which is compounded of the ratios of the sides ; for the vulgar reading, " which is compounded of their sides," is absurd. But, iu this... | |
 | Euclid - 1835 - 540 pages
...of the sides. And to this demonstration agrees the enunciation which is at present in the text, viz. Equiangular parallelograms have to one another the ratio which is compounded of the ratios of the sides : For the vulgar reading, " which is compounded of their sides," is absurd. But, in this... | |
 | John Martin Frederick Wright - Mathematics - 1836 - 776 pages
...which the other sides of the triangle have to one another. Shew that the converse is also true. 2. Equiangular parallelograms have to one another the...which is compounded of the ratios of their sides. 3. The rectangle contained by the diagonals of any quadrilateral figure inscribed in a circle is equal... | |
 | John Playfair - Geometry - 1836 - 148 pages
...equal to GH ; AB is to CD, as EF to GH. If therefore four straight lines, &c. QED PROP. XXIII. THEOR. Equiangular parallelograms have to one another the...which is compounded of the ratios of their sides. Let AC, CF be equiangular parallelograms, having the angle BCD equal to the angle ECG ; the ratio of... | |
 | Mathematics - 1836 - 488 pages
...straight lines be proportionals, those straight lines shall be proportionals. XXIII. Equian. guiar parallelograms have to one another the ratio which is compounded of the ratios of their sides. XXIV. The parallelograms about the diameter of any parallelogram, are similar to the whole, and to... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...squares are proportional, and conversely. For squares are similar figures. PROPOSITION XXIII. THEOREM. Equiangular parallelograms have to one another the...which is compounded of the ratios of their sides. Let AC, CF, he equiangular parallelograms, having the angle BCD equal to the angle ECG ; the ratio... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...&c.* Cor. Triangles which have one angle of the one equal, or supplemental, to one angle of the other, have to one another the ratio which is compounded of the ratios of the sides containing those angles. For, if BD and EG be joined, the triangles BCD, ECG being (I. 84.)... | |
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Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. 
