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 σελίδες |
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Σελίδα 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 ...
Σελίδα 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 ...
Σελίδα 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 ...
Σελίδα 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 ...
Σελίδα 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 Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2022 |
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Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 99 - BAC was proved to be equal to ACD : Therefore the whole angle ACE is equal to the two angles ABC, BAC...
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.