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 Seiten |
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Seite 6
... described from any centre , at any distance from that centre . AXIOM S. I. HINGS which are equal to the fame thing are equal to one another . TH II . If equals be added to equals , the wholes are equal . III . If equals be taken from ...
... described from any centre , at any distance from that centre . AXIOM S. I. HINGS which are equal to the fame thing are equal to one another . TH II . If equals be added to equals , the wholes are equal . III . If equals be taken from ...
Seite 8
... described upon the gi- ven straight line AB . Which was required to be done . om . F PROP . II . PROB . ROM a given point to draw a straight line equal to a given ftraight line . Let A be the given point , and BC the given ftraight line ...
... described upon the gi- ven straight line AB . Which was required to be done . om . F PROP . II . PROB . ROM a given point to draw a straight line equal to a given ftraight line . Let A be the given point , and BC the given ftraight line ...
Seite 9
... described the circle CGH , and from the centre D , at the distance DG , defcribe the circle GKL . AL fhall be equal to BC . Because the point B is the centre of the circle CGH , BC is equal e to BG ; and becaufe D is the Book I. a 1 ...
... described the circle CGH , and from the centre D , at the distance DG , defcribe the circle GKL . AL fhall be equal to BC . Because the point B is the centre of the circle CGH , BC is equal e to BG ; and becaufe D is the Book I. a 1 ...
Seite 45
... described equal to the given rectilineal figure ABCD , having the angle FKM equal to the given angle E. Which was to be done . COR . From this it is manifeft how to a given ftraight line to apply a parallelogram , which fhall have an ...
... described equal to the given rectilineal figure ABCD , having the angle FKM equal to the given angle E. Which was to be done . COR . From this it is manifeft how to a given ftraight line to apply a parallelogram , which fhall have an ...
Seite 46
... described upon the fide BC is equal to the fquares defcribed upon BA , AC . On BC describe a the fquare BDEC , and on BA , AC the fquares GB , HC ; and through A draw b AL parallel to BD or CE , and join AD , FC ; then , because each of ...
... described upon the fide BC is equal to the fquares defcribed upon BA , AC . On BC describe a the fquare BDEC , and on BA , AC the fquares GB , HC ; and through A draw b AL parallel to BD or CE , and join AD , FC ; then , because each of ...
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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
Beliebte Passagen
Seite 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...
Seite 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.
Seite 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.
Seite 9 - Wherefore, from the given point A, a straight line AL has been drawn equal to the given straight line BC.
Seite 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.
Seite 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.
Seite 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.
Seite 6 - Let it be granted that a straight line may be drawn from any one point to any other point.
Seite 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...
Seite 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...