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, 1795 - 400 Seiten |
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Seite 129
... Ratio is a mutual relation of two magnitudes of the same kind to one another , in respect of quantity . IV . Magnitudes are said to be of the same kind , when the less can be multiplied so as to exceed the greater ; and it is only fuch ...
... Ratio is a mutual relation of two magnitudes of the same kind to one another , in respect of quantity . IV . Magnitudes are said to be of the same kind , when the less can be multiplied so as to exceed the greater ; and it is only fuch ...
Seite 130
... same ratio to the second that the third has to the fourthi and the third to the fourth the same ratio which the fifth has to the fixth , and so on , whatever be their number . When four magnitudes , A , B , C , D are proportionals ...
... same ratio to the second that the third has to the fourthi and the third to the fourth the same ratio which the fifth has to the fixth , and so on , whatever be their number . When four magnitudes , A , B , C , D are proportionals ...
Seite 131
... same kind , the first is faid to have to the last of them the ratio com- pounded of the ratio which the first has to the fecond , and of the ratio which the second has to the third , and of the ratio which the third has to the fourth ...
... same kind , the first is faid to have to the last of them the ratio com- pounded of the ratio which the first has to the fecond , and of the ratio which the second has to the third , and of the ratio which the third has to the fourth ...
Seite 132
... ratio which is compounded of three equal ratios is said to be triplicate of any one of these ratios ; and a ratio ... same ratio to the third , which the second has to the fourth ; or that the first is to the third , as the second ...
... ratio which is compounded of three equal ratios is said to be triplicate of any one of these ratios ; and a ratio ... same ratio to the third , which the second has to the fourth ; or that the first is to the third , as the second ...
Seite 135
... ratio of A to B is less than that of C to D. er en B. ed ΑΧΙOMS . : I. FQUIMULTIPLES of the fame , or of equal magnitudes , are equal to one another . II . Those magnitudes of which the same ... same multiple of a less . IV . That ...
... ratio of A to B is less than that of C to D. er en B. ed ΑΧΙOMS . : I. FQUIMULTIPLES of the fame , or of equal magnitudes , are equal to one another . II . Those magnitudes of which the same ... same multiple of a less . IV . That ...
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ABCD alfo alſo alſo equal angle ABC angle ACB angle BAC arch baſe baſe BC BC is equal becauſe becauſe the angle biſected Book VII caſe cauſe centre circle ABC circumference co-fine demonſtrated deſcribed diameter draw drawn equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fame reaſon fides fimilar fince firſt folid fore given ſtraight line greater inſcribed interfect join leſs Let ABC line BC magnitudes oppoſite parallel parallelepiped parallelogram paſs paſſes perpendicular plane polygon priſm proportionals propoſition Q. E. D. PROP radius rectangle contained rectilineal figure remaining angle right angles ſame ſame manner ſame ratio ſecond ſection ſegment ſhall be equal ſhewn ſide ſolid ſpace ſpherical triangle ſquare of AC ſtand ſuch ſum ſuppoſed tangent THEOR theſe thoſe touches the circle triangle ABC wherefore
Beliebte Passagen
Seite 19 - 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...