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 viii
... double the triangle , and then take its half . I cannot agree with Mr Simpson in leaving out the corollaries from prop . 32. nor can I find any reafon for his fo doing . Book II . I have varied the enunciation of feveral of the pro ...
... double the triangle , and then take its half . I cannot agree with Mr Simpson in leaving out the corollaries from prop . 32. nor can I find any reafon for his fo doing . Book II . I have varied the enunciation of feveral of the pro ...
Página 4
... double one and the fame thing are equal be- tween themselves . VII . Things which are half one and the fame thing are equal between themselves . VIII . Things which mutually agree together are equal to one another . IX . Any whole is ...
... double one and the fame thing are equal be- tween themselves . VII . Things which are half one and the fame thing are equal between themselves . VIII . Things which mutually agree together are equal to one another . IX . Any whole is ...
Página 19
... double the number of fides ; but the in- ward angles are equal to double the number of fides , abating four : Therefore the outward are equal to four right angles . I PRO P. XXXIII . THE OR . F two right lines join two equal and ...
... double the number of fides ; but the in- ward angles are equal to double the number of fides , abating four : Therefore the outward are equal to four right angles . I PRO P. XXXIII . THE OR . F two right lines join two equal and ...
Página 20
... double the triangle DBC ; therefore e- qual to one another . If AD is less than AE , add DE to both ; then the whole AE is equal to DF , DC to AB , and the angle FDC to EAB : Therefore the triangles FDC , EAB , are equal . Take DGE from ...
... double the triangle DBC ; therefore e- qual to one another . If AD is less than AE , add DE to both ; then the whole AE is equal to DF , DC to AB , and the angle FDC to EAB : Therefore the triangles FDC , EAB , are equal . Take DGE from ...
Página 22
... double the triangle ABC " ; and therefore double EBC . Wherefore , & c . PROP . XLII . PRO B. O conftitute a parallelogram equal to a given triangle , ha- ving an angle in it equal to a given right lined angle . T % Let the given ...
... double the triangle ABC " ; and therefore double EBC . Wherefore , & c . PROP . XLII . PRO B. O conftitute a parallelogram equal to a given triangle , ha- ving an angle in it equal to a given right lined angle . T % Let the given ...
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The Elements of Euclid: In Which the Propositions Are Demonstrated in a New ... Euclid Sin vista previa disponible - 2022 |
The Elements of Euclid: In Which the Propositions Are Demonstrated in a New ... Euclid Sin vista previa disponible - 2022 |
The Elements of Euclid: In Which the Propositions Are Demonstrated in a New ... Euclid Sin vista previa disponible - 2015 |
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.