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 |
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Results 1-5 of 15
Page 37
... ABC be the given circle , CD the line paffing through the centre , cutting the right line AB , not paffing through the centre , into two equal parts , it will cut it at right angles ; and if the angles AFE , EFB , be right angles , AF ...
... ABC be the given circle , CD the line paffing through the centre , cutting the right line AB , not paffing through the centre , into two equal parts , it will cut it at right angles ; and if the angles AFE , EFB , be right angles , AF ...
Page 38
... circles ABC , CDG , cut each other , they cannot have the fame center . If poffible , let E be the center of both , draw CE to the point of section C , and EFG through any other point ; then , because E is the center of the circle ABC ...
... circles ABC , CDG , cut each other , they cannot have the fame center . If poffible , let E be the center of both , draw CE to the point of section C , and EFG through any other point ; then , because E is the center of the circle ABC ...
Page 50
... circle be compleated , the fegment ABC is greater than a femicircle , and the angle ABC in it lefs than a right ... ABCD in the point B ; from any point D , in the circle , draw the right line DB ; then the angle DBF is equal to the ...
... circle be compleated , the fegment ABC is greater than a femicircle , and the angle ABC in it lefs than a right ... ABCD in the point B ; from any point D , in the circle , draw the right line DB ; then the angle DBF is equal to the ...
Page 52
... circle ABC , that fhall contain an angle equal to the given angle D. Draw the line EF , touching the circle in B ... ABCD , mu- tually cut each other in E ; then the rectangle under AE , EC , is equal to the rectangle under DE , EB ; if ...
... circle ABC , that fhall contain an angle equal to the given angle D. Draw the line EF , touching the circle in B ... ABCD , mu- tually cut each other in E ; then the rectangle under AE , EC , is equal to the rectangle under DE , EB ; if ...
Page 58
... circle about the triangle ABC . Bifect the fides AB , AC , in the points D , E , from which draw DF , FE , at right ... ABCD . Draw the two diameters AC , BD , of the circle , cutting each other at right angles ; and through the points A ...
... circle about the triangle ABC . Bifect the fides AB , AC , in the points D , E , from which draw DF , FE , at right ... ABCD . Draw the two diameters AC , BD , of the circle , cutting each other at right angles ; and through the points A ...
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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.