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 103
... cylinder are the circles defcribed by the motion of the two opposite fides of the parallelogram . XXIV . Similar cones and cylinders are fuch , whofe axes and diameters of their bafes are proportional . XXV . A cube is a folid figure ...
... cylinder are the circles defcribed by the motion of the two opposite fides of the parallelogram . XXIV . Similar cones and cylinders are fuch , whofe axes and diameters of their bafes are proportional . XXV . A cube is a folid figure ...
Seite 138
... cylinder , having the fame bafe , and an equal altitude . Let there be a cone and cylinder , having the same base , viz . the circle ABCD , and their altitudes equal , then the cone is one third of the cylinder ; that is , the cylinder ...
... cylinder , having the fame bafe , and an equal altitude . Let there be a cone and cylinder , having the same base , viz . the circle ABCD , and their altitudes equal , then the cone is one third of the cylinder ; that is , the cylinder ...
Seite 139
... cylinder is not less than triple the cone . Therefore , fince nei- ther greater nor less , it must be triple the cone . Wherefore , & c . PROP . XI . THEOR . ONES and cylinders , of the fame altitude , are to one ano◅ ther , as their ...
... cylinder is not less than triple the cone . Therefore , fince nei- ther greater nor less , it must be triple the cone . Wherefore , & c . PROP . XI . THEOR . ONES and cylinders , of the fame altitude , are to one ano◅ ther , as their ...
Seite 140
... cylinder to cylinder f . Wherefore , & c . PRO P. XII . THE OR . SIMILAR cones and cylinders are to one another , in the tri- plicate ratio of the diameters of their bafes . Let there be fimilar cones and cylinders , whofe bafes are the ...
... cylinder to cylinder f . Wherefore , & c . PRO P. XII . THE OR . SIMILAR cones and cylinders are to one another , in the tri- plicate ratio of the diameters of their bafes . Let there be fimilar cones and cylinders , whofe bafes are the ...
Seite 141
... cones ABCDL , EFGHN , have to one another the triplicate ra- tio of their bafes BD to FH ; and , as cone is to cone , fo is cy- linder to cylinder . Wherefore , & c . e 15. S : 1 PROP . PROP . XIII . THE OR . 7 Book XII OF EUCLID . 141.
... cones ABCDL , EFGHN , have to one another the triplicate ra- tio of their bafes BD to FH ; and , as cone is to cone , fo is cy- linder to cylinder . Wherefore , & c . e 15. S : 1 PROP . PROP . XIII . THE OR . 7 Book XII OF EUCLID . 141.
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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.