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 sider |
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Resultat 1-5 av 14
Side 5
... described an equilateral triangle ABC : Which was required . A PRO P. II . PRO B. ས T a given point to put a right line equal to a given right line . Let A be the given point , and BC the given right line , it is required to put a right ...
... described an equilateral triangle ABC : Which was required . A PRO P. II . PRO B. ས T a given point to put a right line equal to a given right line . Let A be the given point , and BC the given right line , it is required to put a right ...
Side 24
... . £ 29 . IN PRO P. XLVII . T HE OR . every right angled triangle the square described upon the fide fubtending the right angle is equal to the squares of the fides con- taining the right angle . Let A 1 Def . 12 . Def . 26 . 24 THE ...
... . £ 29 . IN PRO P. XLVII . T HE OR . every right angled triangle the square described upon the fide fubtending the right angle is equal to the squares of the fides con- taining the right angle . Let A 1 Def . 12 . Def . 26 . 24 THE ...
Side 55
... described about a right lined fi- gure , when every one of the fides of the circumfcribed figure touches each of the angles of the right lined figure . III . A right lined figure is infcribed in a circle when each of the angles of the ...
... described about a right lined fi- gure , when every one of the fides of the circumfcribed figure touches each of the angles of the right lined figure . III . A right lined figure is infcribed in a circle when each of the angles of the ...
Side 62
... described , it will touch the fides of the pentagon in the points G , H , K , L , M ; wherefore the circle GHKLM is infcribed in the equila- teral and equiangular pentagon ABCDE : Which was res quired . COR COR . If two of the nearest ...
... described , it will touch the fides of the pentagon in the points G , H , K , L , M ; wherefore the circle GHKLM is infcribed in the equila- teral and equiangular pentagon ABCDE : Which was res quired . COR COR . If two of the nearest ...
Side 63
... described about the circle , as may be proved in the same manner as the pentagon : And fo likewife a circle may be inscribed and described about a given hexagon . a 15 . b II . PRO P. XVI . PRO B. то To infcribe an equilateral and ...
... described about the circle , as may be proved in the same manner as the pentagon : And fo likewife a circle may be inscribed and described about a given hexagon . a 15 . b II . PRO P. XVI . PRO B. то To infcribe an equilateral and ...
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Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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...
Side 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.
Side 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.
Side 99 - BAC was proved to be equal to ACD : Therefore the whole angle ACE is equal to the two angles ABC, BAC...
Side 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.
Side 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...
Side 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.
Side 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.
Side 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...
Side 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.