The Elements of Euclid,: In which the Propositions are Demonstrated in a New and Shorter Manner Than in Former Translations, and the Arrangement of Many of Them Altered, to which are Annexed Plain and Spherical Trigonometry, Tables of Logarithms from 1 to 10000, and Tables of Sines, Tangents, and Secants, Both Natural and ArtificialJ. Murray, no. 32. Fleetstreet; and C. Elliot, Parliament-square, Edinburgh., 1776 - 264 sider |
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Side 66
... fourth , when there are taken any equimultiples of the first and third , and likewife any equi- multiples of the fecond and fourth ; if the multiple of the firft , be equal to the multiple of the fecond , then the multiple of the third ...
... fourth , when there are taken any equimultiples of the first and third , and likewife any equi- multiples of the fecond and fourth ; if the multiple of the firft , be equal to the multiple of the fecond , then the multiple of the third ...
Side 67
... fourth ; the first to the fecond is faid to have a greater ratio than the third to the fourth . VIII . Analogy is a fimilitude of proportions . IX . Analogy , at least , consists of three terms . X. When three magnitudes are ...
... fourth ; the first to the fecond is faid to have a greater ratio than the third to the fourth . VIII . Analogy is a fimilitude of proportions . IX . Analogy , at least , consists of three terms . X. When three magnitudes are ...
Side 68
... fourth ; and if the fifth be the fame multiple of the fecond , that the fixth is of the fourth ; then shall the first , added to the fifth , be the fame multiple of the fecond , that the third , added to the fixth , is of the fourth ...
... fourth ; and if the fifth be the fame multiple of the fecond , that the fixth is of the fourth ; then shall the first , added to the fifth , be the fame multiple of the fecond , that the third , added to the fixth , is of the fourth ...
Side 69
... fourth , and there be taken equimultiples of the first and third , then will the magnitudes fo taken be equimultiples of the fecond and fourth . Let the first A be the fame multiple of the fecond B that the third C is of the fourth D ...
... fourth , and there be taken equimultiples of the first and third , then will the magnitudes fo taken be equimultiples of the fecond and fourth . Let the first A be the fame multiple of the fecond B that the third C is of the fourth D ...
Side 74
... fourth ; and if the third has a greater proportion to the fourth , than the fifth to the fixth ; then shall also the first have a greater proportion to the fecond , than the fifth to the fixth . Let the firft A have the fame proportion ...
... fourth ; and if the third has a greater proportion to the fourth , than the fifth to the fixth ; then shall also the first have a greater proportion to the fecond , than the fifth to the fixth . Let the firft A have the fame proportion ...
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Vanlige uttrykk og setninger
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Populære avsnitt
Side 93 - 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...
Side 78 - ... viz. as A is to B, fo is E to F, and B to C as D to E ; and if the firft A be greater than the third C, then the fourth D will be greater than the fixth F ; if equal, equal ; and, if lefs, lefs.
Side 88 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 99 - BAC was proved to be equal to ACD : Therefore the whole angle ACE is equal to the two angles ABC, BAC...
Side 19 - From this it is manifest that if one angle of a triangle be equal to the other two it is a right angle, because the angle adjacent to it is equal to the same two ; (i.
Side 75 - Let AB be the fame multiple of C, that DE is of F : C is to F, as AB to DE. Becaufe AB is the fame multiple of C that DE is of F ; there are as many magnitudes in AB equal to C, as there are in DE equal...
Side 88 - ... reciprocally proportional, are equal to one another. Let AB, BC be equal parallelograms which have the angles at B equal, and let the sides DB, BE be placed in the same straight line ; wherefore also FB, BG are in one straight line (2.
Side 99 - BGC: for the same reason, whatever multiple the circumference EN is of the circumference EF, the same multiple is the angle EHN of the angle EHF: and if the circumference BL be equal to the circumference EN, the angle BGL is also equal to the angle EHN ; (in.
Side 106 - ... but BD, BE, which are in that plane, do each of them meet AB ; therefore each of the angles ABD, ABE is a right angle ; for the same reason, each of the angles CDB, CDE is a right angle: and because AB is equal to DE, and BD...
Side 73 - RATIOS that are the same to the same ratio, are the same to one another. Let A be to B as C is to D ; and as C to D, so let E be to F ; A is to B, as E to F.