| Robert Simson - 1835 - 513 Seiten
...AB is to CD, as EF to GH. " If, therefore, four straight lines, &c. QED PROP. XXIII. THEOR. See N. **Equiangular parallelograms have to one another the...the same with the ratio which is compounded of the** ratio of their sides. Let BC, CG be placed in a straight line ; therefore DC Book vI. and'CE are also... | |
| Euclid - 1835 - 540 Seiten
...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... | |
| 1835
...37. Cor. 4.) ; therefore, the ratio which is compounded of the ratios of CD2 to QN2 and NA= to PT» **is the same with the ratio which is compounded of the ratios of** CP3 to CNa — С P- and С N - to С Р2, the same, that is, with the ratio of G N2 to С N2 - С... | |
| John Playfair - 1836 - 488 Seiten
...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...the parallelogram AC to the parallelogram CF is the** saine with the ratio which is compoundgd of the ratios of their sides. Book VI. Let BC, CG be placed... | |
| John Martin Frederick Wright - 1836 - 776 Seiten
...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 - 472 Seiten
...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 - 114 Seiten
...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... | |
| A. Bell - 1837 - 164 Seiten
...which is compounded of the ratios of the solid AF to the solid GS, and Of the solid GS to the solid GO, **is the same with the ratio which is compounded of the ratios of** the base AC to the base GK, and of the altitude AE to the altitude GM (PI. Ge. V. E). But the ratio... | |
| Euclid - 1837 - 410 Seiten
...&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 - 240 Seiten
...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... | |
| |