Elements of Geometry;: Containing the First Six Books of Euclid, with Two Books on the Geometry of Solids. To which are Added, Elements of Plane and Spherical TrigonometryBell & Bradfute, and G. G. & J. Robinson, London., 1795 - 400 páginas |
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Página 109
... through each . III . A rectilineal figure is faid to be in- scribed in a circle , when all the angles of the inscribed figure are upon the circumference of the circle . Book IV . IV . a 3. I. A rectilineal IV . ELEMENTS ...
... through each . III . A rectilineal figure is faid to be in- scribed in a circle , when all the angles of the inscribed figure are upon the circumference of the circle . Book IV . IV . a 3. I. A rectilineal IV . ELEMENTS ...
Página 111
... to the remaining angle EDF : Wherefore the triangle d 32. 1 . ABC is equiangular to the triangle DEF , and it is inscribed in the circle ABC . Which was to be done . PROP . Book IV . a 23. I. PROP . III . OF GEOMETRY . III.
... to the remaining angle EDF : Wherefore the triangle d 32. 1 . ABC is equiangular to the triangle DEF , and it is inscribed in the circle ABC . Which was to be done . PROP . Book IV . a 23. I. PROP . III . OF GEOMETRY . III.
Página 113
... inscribe à circle in ABC . Bifect a the angles ABC , BCA by the ftraight lines BD , a 9. 1 . CD meeting one another in the point D , from which draw b b 12. 1 . DE , DF , DG perpendiculars Co AB , BC , CA : And be- cause the angle EBD ...
... inscribe à circle in ABC . Bifect a the angles ABC , BCA by the ftraight lines BD , a 9. 1 . CD meeting one another in the point D , from which draw b b 12. 1 . DE , DF , DG perpendiculars Co AB , BC , CA : And be- cause the angle EBD ...
Página 115
... inscribe a fquare in ABCD . Draw the diameters AC , BD at right angles to one ano- ther , and join AB , BC , CD , DA ; becaufe BE is equal to ED , E being the centre , and be- cause EA is at right angles to BD , and common to the ...
... inscribe a fquare in ABCD . Draw the diameters AC , BD at right angles to one ano- ther , and join AB , BC , CD , DA ; becaufe BE is equal to ED , E being the centre , and be- cause EA is at right angles to BD , and common to the ...
Página 120
... and equiangular pentagon has been inscribed . Which was to be done . & PRO P. XII . PROB . O defcribe an equilateral and equiangular pen- tagon about a given circle . f Let Let ABCDE be the given circle , it is required 120 ELEMENTS.
... and equiangular pentagon has been inscribed . Which was to be done . & PRO P. XII . PROB . O defcribe an equilateral and equiangular pen- tagon about a given circle . f Let Let ABCDE be the given circle , it is required 120 ELEMENTS.
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Elements of Geometry: Containing the First Six Books of Euclid, with a ... Formerly Chairman Department of Immunology John Playfair Sin vista previa disponible - 2015 |
Términos y frases comunes
ABCD adjacent angles alfo alfo equal alſo angle ABC angle ACB angle BAC arch bafe baſe BC is equal becauſe the angle bifected Book VII cafe centre circle ABC circumference co-fine defcribed demonftrated diameter draw drawn equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle faid fame manner fame ratio fame reaſon fecond fection fegment femicircle fhewn fimilar fince firft firſt folid fore fquare of AC ftraight line AB fuch given ſtraight line greater impoffible infcribed interfection join lefs leſs Let ABC line BC magnitudes muſt oppofite angle parallel parallelepiped parallelogram perpendicular polygon prifm propofition proportionals radius rectangle contained rectilineal figure remaining angle right angles ſpace ſpherical triangle ſquare tangent thefe THEOR theſe thoſe touches the circle triangle ABC wherefore
Pasajes populares
Página 18 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Página 155 - 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 17 - If, at a point in a straight line, two other straight lines upon the opposite sides of it, make the adjacent angles, together equal to two right angles, these two straight lines shall be in one and the same straight line.
Página 9 - Wherefore, from the given point A, a straight line AL has been drawn equal to the given straight line BC.
Página 3 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Página 23 - Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Página 12 - ABC: and it has also been proved that the angle FBC is equal to the angle GCB, which are the angles upon the other side of the base. Therefore the angles at the base, &c.
Página 6 - Let it be granted that a straight line may be drawn from any one point to any other point.
Página 156 - But by the hypothesis, it is less than a right angle ; which is absurd. Therefore the angles ABC, DEF are not unequal, that is, they are equal : And the angle at A is equal to the angle at D ; wherefore...
Página 44 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced...