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 38
... half of the parallelogram EBCA , because the diameter 34 IAB bifects c it ; and the triangle DBC is the half of the paral- lelogram DBCF , because the diameter DC bifects it : But the d7 . Ax . halves of equal things are equal d ...
... half of the parallelogram EBCA , because the diameter 34 IAB bifects c it ; and the triangle DBC is the half of the paral- lelogram DBCF , because the diameter DC bifects it : But the d7 . Ax . halves of equal things are equal d ...
Página 39
... half of the parallelogram GBCA , because the 34. I. diameter AB bifects it ; and the triangle DEF is the half of the parallelogram DEFH , because the diameter DF bifects it : But the halves of equal things are equal d ; therefore the d ...
... half of the parallelogram GBCA , because the 34. I. diameter AB bifects it ; and the triangle DEF is the half of the parallelogram DEFH , because the diameter DF bifects it : But the halves of equal things are equal d ; therefore the d ...
Página 53
... half the line . Let the ftraight line AB be divided into two equal parts in the point C , and into two unequal parts at the point D ; the rectangle AD , DB , together with the fquare of CD , is equal to the fquare of CB . Upon CB ...
... half the line . Let the ftraight line AB be divided into two equal parts in the point C , and into two unequal parts at the point D ; the rectangle AD , DB , together with the fquare of CD , is equal to the fquare of CB . Upon CB ...
Página 54
... half the line bisected , is equal to the fquare of the ftraight line which is made up of the half and the part produced . Let the straight line AB be bifected in C , and produced to the point D ; the rectangle AD , DB , together with ...
... half the line bisected , is equal to the fquare of the ftraight line which is made up of the half and the part produced . Let the straight line AB be bifected in C , and produced to the point D ; the rectangle AD , DB , together with ...
Página 57
... . From the demonftration it is manifeft , that fince " the fquare of CD is quadruple of the fquare of CB , the " fquare of any line is quadruple of the fquare of half that " line . " PROP . Book IL a II . I. b 31. 1 . OF GEOMETRY . 57.
... . From the demonftration it is manifeft , that fince " the fquare of CD is quadruple of the fquare of CB , the " fquare of any line is quadruple of the fquare of half that " line . " PROP . Book IL a II . I. b 31. 1 . OF GEOMETRY . 57.
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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...