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 Seiten |
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Seite vii
... greater eale to the ftudent . That the reader may be the better prepared for the alterations he may meet with , I have here mentioned a few , with the rea- fons which induced me to make them . Book ; Book I. ax . 10. " Two right lines ...
... greater eale to the ftudent . That the reader may be the better prepared for the alterations he may meet with , I have here mentioned a few , with the rea- fons which induced me to make them . Book ; Book I. ax . 10. " Two right lines ...
Seite xii
... 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 three plane angles , e- qual and fimilar to one another , then it can be divided into angles ...
... 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 three plane angles , e- qual and fimilar to one another , then it can be divided into angles ...
Seite 2
... greater than a right one . XII . An acute angle is that which is less than a right one . XIII . A term , or bound , is the extreme of any thing . XIV . A figure is that which is contained under one or more terms . XV . A circle is a ...
... greater than a right one . XII . An acute angle is that which is less than a right one . XIII . A term , or bound , is the extreme of any thing . XIV . A figure is that which is contained under one or more terms . XV . A circle is a ...
Seite 6
... 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 A , with the distance AD , defcribe a circle ...
... 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 A , with the distance AD , defcribe a circle ...
Seite 7
... greater ; from which cut off DB equal to AC , and join DC ; H then , because DB is equal to AC , the two fides DB , BC , are equal to the two fides AC , BC , and the angles ACB , DBC , e- qual ; therefore the bafe AB is equal to the ...
... greater ; from which cut off DB equal to AC , and join DC ; H then , because DB is equal to AC , the two fides DB , BC , are equal to the two fides AC , BC , and the angles ACB , DBC , e- qual ; therefore the bafe AB is equal to the ...
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Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 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...
Seite 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.
Seite 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.
Seite 99 - BAC was proved to be equal to ACD : Therefore the whole angle ACE is equal to the two angles ABC, BAC...
Seite 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.
Seite 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...
Seite 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.
Seite 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.
Seite 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...
Seite 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.