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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Page x
... folid , are equal and fimilar to the three triangles FAB , FBC , FCA , containing the other folid , and having the common base ABC ; he does not deny the equality of these fo- lids , but compares them with another folid contained by ...
... folid , are equal and fimilar to the three triangles FAB , FBC , FCA , containing the other folid , and having the common base ABC ; he does not deny the equality of these fo- lids , but compares them with another folid contained by ...
Page xi
... folid angles contained by more than three plane angles , are equal and fimilar to one another . " But this prop . C. will e- vidently appear infufficient to supply this fuppofed defect , on ac- count of the limited fenfe in which it is ...
... folid angles contained by more than three plane angles , are equal and fimilar to one another . " But this prop . C. will e- vidently appear infufficient to supply this fuppofed defect , on ac- count of the limited fenfe in which it is ...
Page xii
... folid EABC is not equal to the folid FABC , let it be equal to fome folid as GA BC , either greater or less than EABC , which cannot be ; for the one would contain the other ; and if the folid angle is con- B G E D tained by more than ...
... folid EABC is not equal to the folid FABC , let it be equal to fome folid as GA BC , either greater or less than EABC , which cannot be ; for the one would contain the other ; and if the folid angle is con- B G E D tained by more than ...
Page 101
... folid , is a fuperficies . III . A right line is perpendicular to a plain , when it makes right angles with all the lines that touch it , and are drawn in the fame plain . IV . A plain is perpendicular to a plain , when all the right ...
... folid , is a fuperficies . III . A right line is perpendicular to a plain , when it makes right angles with all the lines that touch it , and are drawn in the fame plain . IV . A plain is perpendicular to a plain , when all the right ...
Page 102
... folid figures are fuch as are contained by an equal number of fimilar and equal plains . XI . A folid angle is the inclination of more than two right lines that meet in one point , but are not in the fame fuperficies . XII . 74 A ...
... folid figures are fuch as are contained by an equal number of fimilar and equal plains . XI . A folid angle is the inclination of more than two right lines that meet in one point , but are not in the fame fuperficies . XII . 74 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.