Euclide's Elements: The Whole Fifteen Books Compendiously Demonstrated. With Archimedes Theorems of the Sphere and Cylinder, Investigated by the Method of IndivisiblesW. Redmayne, 1714 - 520 σελίδες |
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Σελίδα 209
... Medial line , d hyp , and because AC . H :: H. CB . In numbers , let there be DC , 3. and CB , then fhall the rectangle be DB ( Hq ) wherefore H is v √ 54- 93.def.10 . 6. e 13. 10 . 54. f II . 10 . The note of a medial line is μ , of a ...
... Medial line , d hyp , and because AC . H :: H. CB . In numbers , let there be DC , 3. and CB , then fhall the rectangle be DB ( Hq ) wherefore H is v √ 54- 93.def.10 . 6. e 13. 10 . 54. f II . 10 . The note of a medial line is μ , of a ...
Σελίδα 210
... medial line A , be applied on a ra- tional line BC , it makes the breadth CD ratio- nal , and incommenfura- ble in length to the line BC , whereunto the rectangle BD is applied . Because A is u , a therefore fhall Aq be equal to fome ...
... medial line A , be applied on a ra- tional line BC , it makes the breadth CD ratio- nal , and incommenfura- ble in length to the line BC , whereunto the rectangle BD is applied . Because A is u , a therefore fhall Aq be equal to fome ...
Σελίδα 211
... medial . A. B C Lemma . To find out two right lines medial A , B , commenfurable in length , and alfo two , A , C , commenfurable on → ly in power . a Let A be any p , b take B LA , and e Cá lem : 22 . A. d it appears to be done . 10 ...
... medial . A. B C Lemma . To find out two right lines medial A , B , commenfurable in length , and alfo two , A , C , commenfurable on → ly in power . a Let A be any p , b take B LA , and e Cá lem : 22 . A. d it appears to be done . 10 ...
Σελίδα 212
... medial right lines AB , BC commenfurable only in power , is either rational or medial . — Upon the lines AB , BC , a defcribe the fquares AD , CE ; and upon FG make the rectangles FH , AD , b and IK - AC.b and LM - CE . The fquares AD ...
... medial right lines AB , BC commenfurable only in power , is either rational or medial . — Upon the lines AB , BC , a defcribe the fquares AD , CE ; and upon FG make the rectangles FH , AD , b and IK - AC.b and LM - CE . The fquares AD ...
Σελίδα 213
... medial rectangle AB exceedeth not a me- dial rectangle AC by a rational rectangle DB . heor.7.12 . Upon EF , a make a cor.16.6 . AB , a and EH EG = - AC . The rectangles AB , AC , i . e . EG , EH , bb hyp . are ua ; c therefore FG C 23 ...
... medial rectangle AB exceedeth not a me- dial rectangle AC by a rational rectangle DB . heor.7.12 . Upon EF , a make a cor.16.6 . AB , a and EH EG = - AC . The rectangles AB , AC , i . e . EG , EH , bb hyp . are ua ; c therefore FG C 23 ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABC is given ABCD abfurd alfo given alſo altitude angle ABC angle BAC bafe baſe becauſe bifect circle commenfurable compounded Cone confequently conftr Coroll cube defcribed Demonftr diameter Dodecaedron drawn equilateral faid fame fecond feeing fegment fhall fide figure firft fome Forafmuch fore fphere fquare number fubtended fuch fuperficies fuppofed given by kind given by magnitude given by pofition given magnitude given reafon greater hath Icofaedron infcribed interfection leaft lefs likewife meaſure medial oppofite parallel parallelepipedon parallelogram pentagone perpendicular plane prifms PROP proportion pyramides rectangle refidual line right angles right line AB right line BC right line given Schol Scholium ſhall thefe thofe thoſe triangle ABC whence Wherefore whofe whole
Δημοφιλή αποσπάσματα
Σελίδα 26 - 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.
Σελίδα 406 - ... which, when produced, the perpendicular falls, and the straight line intercepted, without the triangle, between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled triangle, having the obtuse angle ACB, and from the point A let AD be drawn...
Σελίδα 269 - A fphere is a folid figure defcribed by the revolution of a i'emicircle about its diameter, which remains unmoved. XV. The axis of a fphere is the fixed ftraight line about which the femicircle revolves. XVI. The centre of a fphere is the fame with that of the femicircle. XVII. The diameter of a fphere is any ftraight line which pafles through the centre, and is terminated both ways by the fuperficies of the fphere.
Σελίδα 2 - The radius of a circle is a right line drawn from the centre to the circumference.
Σελίδα 1 - Bounds) of a Line, are Points. IV. A Right Line, is that which lietb evenly between its Points.
Σελίδα 269 - ... be less than the other side, an obtuse angled ; and if greater, an acute angled cone. XIX. The axis of a cone is the fixed straight line about which the triangle revolves. XX. The base of a cone is the circle described by that side containing the right angle which revolves. XXI. A cylinder is a solid figure described by the revolution of a right angled parallelogram about one of its sides which remains fixed.
Σελίδα 26 - ... the fum of the remaining angles of the one triangle equal to the fum of the remaining angles of the other. 3 . If one angle in a triangle be right, the other two are equal to a right-angle.
Σελίδα 76 - ... the angular points of the figure about which it is defcribed, each thro' each. III. A rectilineal figure is faid to be infcribed in a circle, when all the angles of the infcribed figure are upon the circumference of the circle.
Σελίδα 77 - ... touch the circumference of the circle. IV A right-lined figure is faid to be defcribed about a circle, when all the fides of the figure which is circumfcribed touch the periphery of the circle V.
Σελίδα 269 - Right Lines that touch one another, and are •not in the fame Superficies: Or, a folid Angle is that which is contained under more than two plane Angles which are not in the fame Superficies, but being all at one Point.