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" EQUIANGULAR parallelograms have to one another the ratio 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 the parallelogram AC to the parallelogram... "
The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick - Seite 128
von Royal Military Academy, Woolwich - 1853
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The Elements of Euclid: viz. the first six books, together with the eleventh ...

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...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

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...
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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

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...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

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...
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Solutions of the Cambridge Problems, from 1800 to 1820, Band 2

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...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

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...
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The Element of Geometry

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...
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Solid and Spherical Geometry and Conic Sections: Being a Treatise on the ...

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...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

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.)...
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Elements of Plane Geometry According to Euclid

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...
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