Euclide's Elements: The Whole Fifteen Books Compendiously Demonstrated. With Archimedes Theorems of the Sphere and Cylinder, Investigated by the Method of Indivisibles |
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Seite 1
A plain Angle is the inclination of two lines the one to the other , the one touching the other in ihe same plain , yet not lying in the same strait line . IX . And if the lines which contain the Angle be right lines , it is called a ...
A plain Angle is the inclination of two lines the one to the other , the one touching the other in ihe same plain , yet not lying in the same strait line . IX . And if the lines which contain the Angle be right lines , it is called a ...
Seite 7
Things which are double to the same third , or to equal things , are equal one to the other . Understand the lame of triple , quadruple , & c . 7. Things which are half of one and the fame thing , or of things equal , are equal the one ...
Things which are double to the same third , or to equal things , are equal one to the other . Understand the lame of triple , quadruple , & c . 7. Things which are half of one and the fame thing , or of things equal , are equal the one ...
Seite 19
1 . fore the whole angle ABC = C. , After the same d 9. ax . manner , shall be ABC SA.Which was to be dem . PRO P. XIX . BE In every triangle ABC , under the greatest angle A is . subtended the greatest fide BC .
1 . fore the whole angle ABC = C. , After the same d 9. ax . manner , shall be ABC SA.Which was to be dem . PRO P. XIX . BE In every triangle ABC , under the greatest angle A is . subtended the greatest fide BC .
Seite 23
1 . same manner let AC be equal to DG , d then wille hypthe angle A be equal to EDG . f9 . ax . 2. Hyp . Let AB be equal to ED . Then I say BC - ÉG , and AC = DG and the angle A -EDG . For if EG be greater than BC , make EI = BC ...
1 . same manner let AC be equal to DG , d then wille hypthe angle A be equal to EDG . f9 . ax . 2. Hyp . Let AB be equal to ED . Then I say BC - ÉG , and AC = DG and the angle A -EDG . For if EG be greater than BC , make EI = BC ...
Seite 24
of the other on the same side , or make the inward angles on the same fide AGH , CHG equal to two right angles , then are the right lines AB , CD parallel . Hyp . 1. Because by Hypothefis the angle AGE 2 25.
of the other on the same side , or make the inward angles on the same fide AGH , CHG equal to two right angles , then are the right lines AB , CD parallel . Hyp . 1. Because by Hypothefis the angle AGE 2 25.
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Euclide's Elements: The Whole Fifteen Books Compendiously Demonstrated: With ... Isaac Barrow,Isaac Euclid,Francois Foix De Candale Keine Leseprobe verfügbar - 2018 |
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ABCD alſo given altitude baſe becauſe circle common compounded Cone conſequently Conſtr contained Coroll cube Demonſtr deſcribed diameter divided double draw drawn equal equilateral fall fame fide figure firſt fore fourth given by kind given by poſition given magnitude given reaſon greater hath Hence join leaſt leſs likewiſe line BC magnitude manner meaſure medial multiplied parallel parallelogram pentagone perpendicular plane prime produced PROP proportion pyramides rational reaſon rectangle remaining reſidual right angles right line ſaid ſame ſay ſecond ſeeing ſegment ſhall ſide ſolid ſpace ſphere ſquare ſuperficies Take taken thence thereof theſe things third thoſe triangle triangle ABC whence Wherefore whole whoſe
Beliebte Passagen
Seite 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.
Seite 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...
Seite 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.
Seite 2 - The radius of a circle is a right line drawn from the centre to the circumference.
Seite 1 - Bounds) of a Line, are Points. IV. A Right Line, is that which lietb evenly between its Points.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Bibliografische Informationen
| Titel | Euclide's Elements: The Whole Fifteen Books Compendiously Demonstrated. With Archimedes Theorems of the Sphere and Cylinder, Investigated by the Method of Indivisibles |
| Autoren | Euclid, Isaac Barrow |
| Herausgeber | Isaac Barrow |
| Verlag | W. Redmayne, 1714 |
| Original von | University of Michigan |
| Digitalisiert | 8. Juni 2007 |
| Länge | 520 Seiten |
| Zitat exportieren | BiBTeX EndNote RefMan |