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 10,000, and Tables of Sines, Tangents, and Secants, Natural and Artificialauthor, and sold, 1776 - 264 sider |
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Side viii
... added a cor . to prop . 17. that convincingly proves it . The 35th and 37th are joined in one , as nothing can follow more naturally than , if the wholes are equal , their halfs are likewife fo . The fame may be faid of the 36th and ...
... added a cor . to prop . 17. that convincingly proves it . The 35th and 37th are joined in one , as nothing can follow more naturally than , if the wholes are equal , their halfs are likewife fo . The fame may be faid of the 36th and ...
Side ix
... added a few words to the 5th def . which renders it compleat ; the lemma added to prop . 22. is therefore unneceffary ; as alfo def . A. inferted after def . 11. book V. by Mr Simpson . The 5th and 6th propofitions are joined in one ...
... added a few words to the 5th def . which renders it compleat ; the lemma added to prop . 22. is therefore unneceffary ; as alfo def . A. inferted after def . 11. book V. by Mr Simpson . The 5th and 6th propofitions are joined in one ...
Side 3
... added to equal things , the wholes will be e- qual . III . If from equal things equal things be taken , the remainders will be equal . IV . If to unequal things equal things are added , the whole will be unequal . V. I Book I. V. If ...
... added to equal things , the wholes will be e- qual . III . If from equal things equal things be taken , the remainders will be equal . IV . If to unequal things equal things are added , the whole will be unequal . V. I Book I. V. If ...
Side 29
... added line for the other fide , together with the fquare of half the line , are equal to the fquare of the half and added line , as one fide of the square . Let the right line AB be bifected in C , and BD added to it , the rectangle ...
... added line for the other fide , together with the fquare of half the line , are equal to the fquare of the half and added line , as one fide of the square . Let the right line AB be bifected in C , and BD added to it , the rectangle ...
Side 31
... added to it , the fquare of the whole and added line taken as one line , and the fquare of the added line , are double the Square of the half line , and double the fquare of the half and added line , taken as one line . Let the right ...
... added to it , the fquare of the whole and added line taken as one line , and the fquare of the added line , are double the Square of the half line , and double the fquare of the half and added line , taken as one line . Let the right ...
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The Elements of Euclid: In Which the Propositions Are Demonstrated in a New ... Euclid Ingen forhåndsvisning - 2015 |
Almindelige termer og sætninger
ABCM angle ABC angle BAC arch bafe bafe BC baſe becauſe bifected 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 reaſon fecond fegment femicircle fhall fides fimilar folid angle folid parallelopipedons fome fore fphere fquare of AC fubtending given right line greater infcribed join lefs leſs likewife magnitudes parallel parallelogram perpendicular plain paffing polygon polyhedron prifms PROP pyramid rectangle right angles right line AB right lined figure Secant Sine Tang tangent thefe THEOR theſe triangle ABC triplicate ratio Wherefore whofe bafe whoſe
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Side 80 - 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 72 - F, equal to them in number, be taken two and two in the fame ratio, and if their analogy be perturbate, 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 91 - BAC was proved to be equal to ACD : Therefore the whole angle ACE is equal to the two angles ABC, BAC...
Side x - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles, these straight lines being continually produced, shall at length meet upon that side on which are the angles which are less than two right angles.
Side 54 - Let ABC be the given circle, and D the given straight line, not greater than the diameter of the circle. It is required to place in the circle ABC a straight line equal to D.
Side 9 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Side 13 - 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 69 - 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...
Side 91 - 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 80 - ... 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.