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 ix
... natural and artificial , which will work to the fame exactnefs , of any extant , even to fecond and third ininutes , or farther , if thought neceflary , Upon Upon the whole , although the above alterations are intended PREFACE . ix.
... natural and artificial , which will work to the fame exactnefs , of any extant , even to fecond and third ininutes , or farther , if thought neceflary , Upon Upon the whole , although the above alterations are intended PREFACE . ix.
Σελίδα 13
... third . In any triangle , ABC , two fides of it , however taken , are greater than the third , viz . AB , AC , greater than BC ; AC , BC , greater than AB ; or BC , AB , greater than AC . For , produce any fide , as BA , to D ; make AD ...
... third . In any triangle , ABC , two fides of it , however taken , are greater than the third , viz . AB , AC , greater than BC ; AC , BC , greater than AB ; or BC , AB , greater than AC . For , produce any fide , as BA , to D ; make AD ...
Σελίδα 14
... third . Let A , B , C , be the three given right lines , any two of which are greater than the third . Take any right line bounded at D , but not bounded at E , from which cut off DF equal to A , FG equal to B , and make GH equal to C ...
... third . Let A , B , C , be the three given right lines , any two of which are greater than the third . Take any right line bounded at D , but not bounded at E , from which cut off DF equal to A , FG equal to B , and make GH equal to C ...
Σελίδα 19
... third of two right angles , or two thirds of one right angle . 6. If one angle of a triangle be equal to the other two , that angle is a right one ; for , if the fide is produced , the adjacent angle is equal to the other two ...
... third of two right angles , or two thirds of one right angle . 6. If one angle of a triangle be equal to the other two , that angle is a right one ; for , if the fide is produced , the adjacent angle is equal to the other two ...
Σελίδα 56
... third d Cor . 32. angles BAC , EDF are equal ; therefore the triangle ABC , is inscribed in the circle ABC , and equiangular to the triangle DEF , which was required . Wherefore , & c . I. d PROP . Book IV . A PROP . III . PRO B. 56 THE ...
... third d Cor . 32. angles BAC , EDF are equal ; therefore the triangle ABC , is inscribed in the circle ABC , and equiangular to the triangle DEF , which was required . Wherefore , & c . I. d PROP . Book IV . A PROP . III . PRO B. 56 THE ...
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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.