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 vi
... definition of proportion- als , except that of EUCLID , has ever been given , from which their properties can be deduced by reafonings , which , at the fame time that they are perfectly rigorous , are alfo fimple and direct . As to the ...
... definition of proportion- als , except that of EUCLID , has ever been given , from which their properties can be deduced by reafonings , which , at the fame time that they are perfectly rigorous , are alfo fimple and direct . As to the ...
Seite vii
... definitions in the first Book , and particularly on that of a ftraight line . A new Axiom is alfo introduced in the room of the 12th , for the purpose of demonftrating more easi- ly fome of the properties of parallel lines . In the ...
... definitions in the first Book , and particularly on that of a ftraight line . A new Axiom is alfo introduced in the room of the 12th , for the purpose of demonftrating more easi- ly fome of the properties of parallel lines . In the ...
Seite xv
... , as he had not been careful in laying the founda- tion , he would never be fuccefsful in raifing the fuperftructure . COLLEGE OF EDINBURGH , Oct. 21. 1795 . ERRATA . Book III . Definitions , for Def . PREFACE .. -XV.
... , as he had not been careful in laying the founda- tion , he would never be fuccefsful in raifing the fuperftructure . COLLEGE OF EDINBURGH , Oct. 21. 1795 . ERRATA . Book III . Definitions , for Def . PREFACE .. -XV.
Seite xvi
... Definitions , for Def . XI . read Def . IX . Book V. Prop . XXIV . line third of the Demonstration , read Because E : B :: F : D , by inverfion , B : E :: C : D . P. 263. fourth line , for a , read two . ELEMENTS OF GEOMETRY . “ A BOOK ...
... Definitions , for Def . XI . read Def . IX . Book V. Prop . XXIV . line third of the Demonstration , read Because E : B :: F : D , by inverfion , B : E :: C : D . P. 263. fourth line , for a , read two . ELEMENTS OF GEOMETRY . “ A BOOK ...
Seite 1
... DEFINITIONS . I. Point is that which has pofition , but not magni- See Notes . tude . " II . A line is length without breadth . COROLLARY . The extremities of a line are points ; and " the intersections of one line with another are also ...
... DEFINITIONS . I. Point is that which has pofition , but not magni- See Notes . tude . " II . A line is length without breadth . COROLLARY . The extremities of a line are points ; and " the intersections of one line with another are also ...
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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...