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 36
... ABCD shall be equal to the parallelogram EBCF . If the fides AD , DF of the A parallelograms ABCD , DBCF oppofite to the base . BC be ter- minated in the fame point D ; it is plain that each of the pa- a 34. I. rallelograms is double a ...
... ABCD shall be equal to the parallelogram EBCF . If the fides AD , DF of the A parallelograms ABCD , DBCF oppofite to the base . BC be ter- minated in the fame point D ; it is plain that each of the pa- a 34. I. rallelograms is double a ...
Seite 37
... ABCD , EFGH A be parallelograms upon equal bafes BC , FG , and between the fame parallels AH , BG ; the parallelogram ABCD is equal to EFGH . Join BE , CH ; and B C F G because BC is equal to FG , and FG to a EH , BC is equal to a 34. I ...
... ABCD , EFGH A be parallelograms upon equal bafes BC , FG , and between the fame parallels AH , BG ; the parallelogram ABCD is equal to EFGH . Join BE , CH ; and B C F G because BC is equal to FG , and FG to a EH , BC is equal to a 34. I ...
Seite 38
... ABCD is equal to EFGH Wherefore parallelograms , & c . QE . D. PROP . XXXVII . THEOR . TRIANGLES upon the fame bafe , and between the fame parallels , are equal to one another . Let the triangles ABC , DBC be upon the fame bafe BC and ...
... ABCD is equal to EFGH Wherefore parallelograms , & c . QE . D. PROP . XXXVII . THEOR . TRIANGLES upon the fame bafe , and between the fame parallels , are equal to one another . Let the triangles ABC , DBC be upon the fame bafe BC and ...
Seite 40
... ABCD and the triangle EBC be upon the fame bafe BC , and between the fame parallels BC , AE ; the parallelogram ABCD is A double of the I AE ; 40 ELEMENTS Book I. ...
... ABCD and the triangle EBC be upon the fame bafe BC , and between the fame parallels BC , AE ; the parallelogram ABCD is A double of the I AE ; 40 ELEMENTS Book I. ...
Seite 41
... ABCD is A double of the triangle EBC . Join AC ; then the triangle ABC is equal a to the triangle EBC , because they are upon the fame base BC , and between the fame parallels BC , AE . But the parallelogram ABCD is double b of the ...
... ABCD is A double of the triangle EBC . Join AC ; then the triangle ABC is equal a to the triangle EBC , because they are upon the fame base BC , and between the fame parallels BC , AE . But the parallelogram ABCD is double b of the ...
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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...