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 viii
... because it follows more naturally as a corollary . The 18th and 19th are joined in one , for the rea- fons already given . I have put a short and natural demonftra- tion in place of the 2d part of prop . tion PREFACE .
... because it follows more naturally as a corollary . The 18th and 19th are joined in one , for the rea- fons already given . I have put a short and natural demonftra- tion in place of the 2d part of prop . tion PREFACE .
Σελίδα x
... because the one contains the other . If he had proved , that the triangles GAB , GBC , GCA , were equal and similar to the other three triangles EAB , EBC , ECA , and common base ABC , and then proved the folids not equal , he would ...
... because the one contains the other . If he had proved , that the triangles GAB , GBC , GCA , were equal and similar to the other three triangles EAB , EBC , ECA , and common base ABC , and then proved the folids not equal , he would ...
Σελίδα 5
... because C is the center of the circle BGH , BCis equal to CG ; and because D is the center of the circle KGL , DGe Def . 15 is equal to DL , but DC is equal to DA : Therefore the re- mainders AL , and CG , are equalf ; but BC , AL , are ...
... because C is the center of the circle BGH , BCis equal to CG ; and because D is the center of the circle KGL , DGe Def . 15 is equal to DL , but DC is equal to DA : Therefore the re- mainders AL , and CG , are equalf ; but BC , AL , are ...
Σελίδα 6
... because A is the center of the circle DEF , AE is equal to AD , but AD'is equal to C : Therefore AE is likewise ... because the angles BAC EDF are equal , the right line AC will coincide with DF , and the point C with F ; for AC ...
... because A is the center of the circle DEF , AE is equal to AD , but AD'is equal to C : Therefore AE is likewise ... because the angles BAC EDF are equal , the right line AC will coincide with DF , and the point C with F ; for AC ...
Σελίδα 8
... because AC , AD , are equal , the angles ADE , ACD are equal ; but the angle BDC is greater than ADCb , or bAx.9 . ACD , and much greater than BCD ; but , if BD is equal to BC , the angles BCD , BDC , are equal , and likewife greater ...
... because AC , AD , are equal , the angles ADE , ACD are equal ; but the angle BDC is greater than ADCb , or bAx.9 . ACD , and much greater than BCD ; but , if BD is equal to BC , the angles BCD , BDC , are equal , and likewife greater ...
Άλλες εκδόσεις - Προβολή όλων
The Elements of Euclid: In Which the Propositions Are Demonstrated in a New ... Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCM angle ABC angle BAC arch baſe BC becauſe biſect Book XI circle ABCD circle EFGH circumference cofine common fection cone contained cylinder DEFH deſcribe diameter draw drawn equal angles equal to AC equiangular equilateral equimultiples fame altitude fame multiple fame plain fame proportion fame reaſon fides fimilar firſt folid angle fore fubtend given right line greater inſcribed join leſs Let ABC likewife magnitudes oppoſite parallel parallelogram perpendicular plain angles polygon priſm PROB PROP pyramid rectangle right angles right lined figure ſame Secant ſecond ſegment ſhall ſide Sine ſolid ſome ſphere ſquare ſquare of AC Tang tangent THEOR theſe triangle ABC triplicate ratio verſed Wherefore whoſe baſe
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.