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 páginas |
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Página 66
... Ratio is a certain mutual habitude of magnitudes of the fame kind , according to quantity . IV . Magnitudes have proportion to each other ; which , being multi- plied , can exceed one another . V. Magnitudes have the fame ratio to each ...
... Ratio is a certain mutual habitude of magnitudes of the fame kind , according to quantity . IV . Magnitudes have proportion to each other ; which , being multi- plied , can exceed one another . V. Magnitudes have the fame ratio to each ...
Página 67
... ratio of what it has to the fecond ; and always one more in order as the proportionals fhall be extend- ed . XII . Homologous magnitudes , or magnitudes of a like ratio , are such whofe antecedents are to the antecedents and confequents ...
... ratio of what it has to the fecond ; and always one more in order as the proportionals fhall be extend- ed . XII . Homologous magnitudes , or magnitudes of a like ratio , are such whofe antecedents are to the antecedents and confequents ...
Página 68
... ratio ; in the first order of magnitudes , as the antecedent is to the confequent ; fo , in the fecond order of magnitudes , is the antecedent to the confequent ; and , as in the first order , the confequent is to fome other , fo , in ...
... ratio ; in the first order of magnitudes , as the antecedent is to the confequent ; fo , in the fecond order of magnitudes , is the antecedent to the confequent ; and , as in the first order , the confequent is to fome other , fo , in ...
Página 69
... ratio to the fecond that the third has to the fourth , then shall also the equimultiples of the first have the fame ratio to the equimultiple of the fecond that the equimultiple of the third has to that of the fourth . Let there be four ...
... ratio to the fecond that the third has to the fourth , then shall also the equimultiples of the first have the fame ratio to the equimultiple of the fecond that the equimultiple of the third has to that of the fourth . Let there be four ...
Página 77
... ratio ; and if the firf magnitude be equal to the third , then the fourth will be equal to the fixth ; and , if the first be greater than the third , then the fourth will be greater than the fixth ; and , if the first be less than the ...
... ratio ; and if the firf magnitude be equal to the third , then the fourth will be equal to the fixth ; and , if the first be greater than the third , then the fourth will be greater than the fixth ; and , if the first be less than the ...
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The Elements of Euclid: In Which the Propositions Are Demonstrated in a New ... Euclid Sin vista previa disponible - 2022 |
The Elements of Euclid: In Which the Propositions Are Demonstrated in a New ... Euclid Sin vista previa disponible - 2022 |
The Elements of Euclid: In Which the Propositions Are Demonstrated in a New ... Euclid Sin vista previa disponible - 2015 |
Términos y frases comunes
ABCM angle ABC angle BAC arch bafe baſe becauſe bifect Book XI circle ABCD circle EFGH circumference cofine common fection cone contained cylinder defcribe DEFH diameter draw drawn equal angles equal to AC equiangular equilateral equimultiples fame altitude fame multiple fame plain fame proportion fame reafon fecond fegment femicircle fides fimilar folid angle fome fore fquare of AC fubtending given right line greater infcribed join lefs leſs Let ABC magnitudes oppofite parallel parallelogram perpendicular plain angles plain paffing polygon prifms Prop pyramid rectangle right angles right line AB right lined figure Secant Sine ſphere ſquare Tang tangent thefe THEOR theſe triangle ABC triplicate ratio Wherefore whofe ΙΟ
Pasajes populares
Página 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...
Página 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.
Página 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.
Página 99 - BAC was proved to be equal to ACD : Therefore the whole angle ACE is equal to the two angles ABC, BAC...
Página 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.
Página 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...
Página 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.
Página 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.
Página 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...
Página 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.