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 Trigonometry |
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Page vi
... 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 defects , on ...
... 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 defects , on ...
Page 130
... proportionals , when the first has the fame ratio to the second that the third has to the fourth and the third to the fourth the fame ratio which the fifth has to the fixth , and so on , whatever be their number . When four magnitudes ...
... proportionals , when the first has the fame ratio to the second that the third has to the fourth and the third to the fourth the fame ratio which the fifth has to the fixth , and so on , whatever be their number . When four magnitudes ...
Page 131
... proportionals , the ratio of A to C is duplicate of that of A to B , er of B to C : For by the last definition , the ratio of A to C is compounded of the ratios of A to B , and of B to C ; but the ratio of A to B is equal to the ratio ...
... proportionals , the ratio of A to C is duplicate of that of A to B , er of B to C : For by the last definition , the ratio of A to C is compounded of the ratios of A to B , and of B to C ; but the ratio of A to B is equal to the ratio ...
Page 132
... proportionals , fo as that they continue still to be proportionals . XIV . Permutando , or alternando , by permutation , or alternately this word is used when there are four proportionals , and it is inferred , that the first has the ...
... proportionals , fo as that they continue still to be proportionals . XIV . Permutando , or alternando , by permutation , or alternately this word is used when there are four proportionals , and it is inferred , that the first has the ...
Page 133
... proportionals , and it is inferred , that the excefs of the firft above the fe- cond , is to the fecond , as the ... proportion- als when taken two and two of each rank , and it is in- ferred , that the first is to the last of the firft ...
... proportionals , and it is inferred , that the excefs of the firft above the fe- cond , is to the fecond , as the ... proportion- als when taken two and two of each rank , and it is in- ferred , that the first is to the last of the firft ...
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Common terms and phrases
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
Popular passages
Page 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...
Page 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.
Page 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.
Page 9 - Wherefore, from the given point A, a straight line AL has been drawn equal to the given straight line BC.
Page 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.
Page 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.
Page 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.
Page 6 - Let it be granted that a straight line may be drawn from any one point to any other point.
Page 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...
Page 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...