 | John Martin Frederick Wright - 1831 - 282 pagina’s
...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... | |
 | 1831 - 532 pagina’s
...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 pagina’s
...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 pagina’s
...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 - 1836 - 776 pagina’s
...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... | |
 | 1836 - 488 pagina’s
...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... | |
 | John Playfair - 1836 - 148 pagina’s
...equal to the angle ECG ; the ratio of the parallelogram AC to the parallelogram CF, is the same with the ratio which is compounded of the ratios of their sides. Let BC, CG, be placed in a straight line ; therefore DC and CE are also in a straight line (2. 1.) ; and... | |
 | Euclid, James Thomson - 1837 - 410 pagina’s
...&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.)... | |
 | Andrew Bell - 1837 - 290 pagina’s
...equal to the angle ECG ; the ratio of the parallelogram AC to the parallelogram CF, is the same with the ratio which is compounded of the ratios of their sides. Let EC, CG, be placed in a straight line ; therefore DC and CE are also in a straight line (I. 14) ; and... | |
 | Robert Simson - 1838 - 434 pagina’s
...and that PR is equal to GH ; AB is to CD, as EF to GH. If, therefore, four straight lines, &c. QED PROP. XXIII. THEOR. EQUIANGULAR parallelograms have...CF be equiangular parallelograms, having the angle * See Note. BCD equal to the angle ECG : the ratio of the parallelogram AC to the parallelogram CF,... | |
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Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. 
