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 páginas |
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Página x
... base ABC ; he does not deny the equality of these fo- lids , but compares them with another folid contained by three triangles GAB , GBC , GCA , and common bafe ABC , which three triangles he neither proves equal nor fimilar ; but ...
... base ABC ; he does not deny the equality of these fo- lids , but compares them with another folid contained by three triangles GAB , GBC , GCA , and common bafe ABC , which three triangles he neither proves equal nor fimilar ; but ...
Página xi
... . He has proved the three triangles EAB , EBC , ECA , containing the one folid , equal and fimilar to the three triangles FAB , FBC , FCA , containing the other fo- lid [ f lid , having the common base , ABC ; PREFACE . xi.
... . He has proved the three triangles EAB , EBC , ECA , containing the one folid , equal and fimilar to the three triangles FAB , FBC , FCA , containing the other fo- lid [ f lid , having the common base , ABC ; PREFACE . xi.
Página xii
... base , ABC ; then , if the 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 ...
... base , ABC ; then , if the 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 ...
Página 6
... base of the one triangle will be equal to the bafe of the other ; the two triangles will be equal , and the remaining angles of the one equal to the remaining angles of the other , each to each , which the equal fides fubtend . Let the ...
... base of the one triangle will be equal to the bafe of the other ; the two triangles will be equal , and the remaining angles of the one equal to the remaining angles of the other , each to each , which the equal fides fubtend . Let the ...
Página 8
... base of the one equal to the base of the other , then the angles that these equal bases fubtend will be equal to one another . Let the two triangles be ABC , DEF , having the two fides AB , AC , equal to the two fides DE , DF , each to ...
... base of the one equal to the base of the other , then the angles that these equal bases fubtend will be equal to one another . Let the two triangles be ABC , DEF , having the two fides AB , AC , equal to the two fides DE , DF , each to ...
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Términos y frases comunes
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
Pasajes populares
Página 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...
Página 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.
Página 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.
Página 99 - BAC was proved to be equal to ACD : Therefore the whole angle ACE is equal to the two angles ABC, BAC...
Página 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.
Página 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...
Página 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.
Página 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.
Página 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...
Página 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.