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 - Geometry - 264 pages |
From inside the book
Results 1-5 of 37
Page 5
... given right line . Let AB be the given right line , upon which it is required to defcribe an equilateral triangle . About the center A , with the distance AB , describe the circle a 3 . BCD 2 ; and about the center B , with the distance ...
... given right line . Let AB be the given right line , upon which it is required to defcribe an equilateral triangle . About the center A , with the distance AB , describe the circle a 3 . BCD 2 ; and about the center B , with the distance ...
Page 6
... right lines being given , to cut off from the greater a part equal to the leffer . Required to cut off from the greater AB a part AE , equal to the leffer C. From the point A draw a right line AD equal to Ca , about Faft . 3. the center ...
... right lines being given , to cut off from the greater a part equal to the leffer . Required to cut off from the greater AB a part AE , equal to the leffer C. From the point A draw a right line AD equal to Ca , about Faft . 3. the center ...
Page 7
... given , having the fides DE , DF , equal to the fides AB , AC , each to each ; and the angle BAC equal to the angle ... right line , to two different points on the fame fide , there be drawn two right lines equal to one another , the ...
... given , having the fides DE , DF , equal to the fides AB , AC , each to each ; and the angle BAC equal to the angle ... right line , to two different points on the fame fide , there be drawn two right lines equal to one another , the ...
Page 8
... right line BC may coincide with EF ; then the point B will coincide with the point E , and C with F ; for the fides ... given right lined angle into two equal parts . Let BAC be the given right lined angle required to be cut into two ...
... right line BC may coincide with EF ; then the point B will coincide with the point E , and C with F ; for the fides ... given right lined angle into two equal parts . Let BAC be the given right lined angle required to be cut into two ...
Page 9
... given finite right line into two equal parts . Let AB be a given right line , required to be cut into two e- qual parts ; upon it defcribe an equilateral triangle ABC ; bi- fect the angle ACB by the right line CD ; then is the right a ...
... given finite right line into two equal parts . Let AB be a given right line , required to be cut into two e- qual parts ; upon it defcribe an equilateral triangle ABC ; bi- fect the angle ACB by the right line CD ; then is the right a ...
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The Elements of Euclid: In Which the Propositions Are Demonstrated in a New ... Euclid No preview available - 2022 |
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Common terms and phrases
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
Popular passages
Page 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...
Page 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.
Page 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.
Page 99 - BAC was proved to be equal to ACD : Therefore the whole angle ACE is equal to the two angles ABC, BAC...
Page 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.
Page 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...
Page 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.
Page 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.
Page 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...
Page 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.