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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Αποτελέσματα 1 - 5 από τα 21.
Σελίδα 1
... magnitude . II . A line is length without breadth . III . The bounds of a line are points : IV . A right line is that which lieth evenly between its points . V. A fuperficies is that which hath only length and breadth . VI The bounds of ...
... magnitude . II . A line is length without breadth . III . The bounds of a line are points : IV . A right line is that which lieth evenly between its points . V. A fuperficies is that which hath only length and breadth . VI The bounds of ...
Σελίδα 66
... 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 other , viz . the first to the fecond ...
... 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 other , viz . the first to the fecond ...
Σελίδα 67
... magnitudes , or magnitudes of a like ratio , are such whofe antecedents are to the antecedents and confequents to the confequents in the fame ratio . XIII . Alternate ratio is the comparing the antecedent with the ante- cedent , and ...
... magnitudes , or magnitudes of a like ratio , are such whofe antecedents are to the antecedents and confequents to the confequents in the fame ratio . XIII . Alternate ratio is the comparing the antecedent with the ante- cedent , and ...
Σελίδα 68
... magnitudes ; and as the confequent is to any other , fo is the confequent to any other . XX . Perturbate proportion ... magnitudes , as the antecedent is to the confequent ; fo , in the fecond order of magnitudes , is the antecedent to ...
... magnitudes ; and as the confequent is to any other , fo is the confequent to any other . XX . Perturbate proportion ... magnitudes , as the antecedent is to the confequent ; fo , in the fecond order of magnitudes , is the antecedent to ...
Σελίδα 69
... magnitudes in BG equal to C , as there are in EH , equal to F ; therefore there are as many magnitudes in AG equal to C , as there are in DH equal to F. Wherefore , & c . a . I. PRO P. III . THE OR . IF the first be the fame multiple of ...
... magnitudes in BG equal to C , as there are in EH , equal to F ; therefore there are as many magnitudes in AG equal to C , as there are in DH equal to F. Wherefore , & c . a . I. PRO P. III . THE OR . IF the first be the fame multiple of ...
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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.