Elements of Geometry;: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids; to which are Added, Elements of Plane and Spherical TrigonometryBell & Bradfute, 1804 - 440 sider |
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Side ix
... fourth propofition is from Legendre's Elements of Geometry ; that of the fixth is new , as far as I know ; as is alfo the folution of the problem in the nineteenth propo- fition ; a problem which , though in itself ex- tremely fimple ...
... fourth propofition is from Legendre's Elements of Geometry ; that of the fixth is new , as far as I know ; as is alfo the folution of the problem in the nineteenth propo- fition ; a problem which , though in itself ex- tremely fimple ...
Side 131
... fourth , equal to it , or lefs ; then the first of the magnitudes is faid to have to the fecond the fame ratio that the third has to the fourth . VI . Magnitudes are faid to be proportionals , when the first has the fame ratio to the ...
... fourth , equal to it , or lefs ; then the first of the magnitudes is faid to have to the fecond the fame ratio that the third has to the fourth . VI . Magnitudes are faid to be proportionals , when the first has the fame ratio to the ...
Side 132
... fourth , and fo on unto the laft magnitude . For example , if A , B , C , D be four magnitudes of the fame kind , the first A is said to have to the last D , the ratio com- pounded of the ratio of A to B , and of the ratio of B to C ...
... fourth , and fo on unto the laft magnitude . For example , if A , B , C , D be four magnitudes of the fame kind , the first A is said to have to the last D , the ratio com- pounded of the ratio of A to B , and of the ratio of B to C ...
Side 133
... fourth ; or that the first is to the third as the fecond to the fourth : See prop . 16th of this book . XV . Invertendo , by inverfion : When there are four proportionals , and it is inferred , that the second is to the first , as the ...
... fourth ; or that the first is to the third as the fecond to the fourth : See prop . 16th of this book . XV . Invertendo , by inverfion : When there are four proportionals , and it is inferred , that the second is to the first , as the ...
Side 134
... fourth , is to the fourth . 18th prop . book 5 . XVII . Dividendo , by divifion : When there are four proportionals , and it is inferred , that the excess of the first above the se- cond , is to the fecond , as the excefs of the third ...
... fourth , is to the fourth . 18th prop . book 5 . XVII . Dividendo , by divifion : When there are four proportionals , and it is inferred , that the excess of the first above the se- cond , is to the fecond , as the excefs of the third ...
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ABC is equal ABCD alfo alſo angle ABC angle ACB angle BAC arch bafe baſe becauſe the angle bifected Book cafe centre circle ABC circumference co-fine cof BC cylinder defcribed demonftrated diameter draw drawn equal angles equiangular equilateral polygon equimultiples Euclid exterior angle faid fame altitude fame manner fame plane fame ratio fame reaſon fecond fection fegment femicircle fhall fhewn fide BC fides fince firft firſt folid fore fquare fuch given ftraight line greater infcribed interfect join lefs leſs Let ABC line BC magnitudes muſt oppofite angle parallel parallelepipeds parallelogram perpendicular polygon prifm propofition proportionals Q. E. D. PROP radius reafon rectangle contained rectilineal figure remaining angle ſpherical triangle ſquare tangent THEOR theſe thofe thoſe triangle ABC uſe wherefore
Populære passager
Side 27 - 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...
Side 172 - 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.
Side 42 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.
Side 84 - The diameter is the greatest straight line in a circle; and of all others, that which is nearer to the centre is always greater than one more remote; and the greater is nearer to the centre than the less. Let ABCD be a circle, of which...
Side 106 - IF from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it ; if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle be equal to the square of the line which meets it, the line which meets shall touch the circle.
Side 22 - THE greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it. Let ABC be a triangle, of which the angle ABC is greater than the angle BCA : the side AC is likewise greater than the side AB. For, if it be not greater, AC must...
Side 64 - If then the sides of it, BE, ED are equal to one another, it is a square, and what was required is now done: But if they are not equal, produce one of them BE to F, and make EF equal to ED, and bisect BF in G : and from the centre G, at the distance GB, or GF, describe the semicircle...
Side 166 - IN a right angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another. Let ABC be a right angled triangle, having the right angle BAC ; and from the point A let AD be drawn perpendicular to the base BC : the triangles ABD, ADC are similar to the whole triangle ABC, and to one another.
Side 54 - 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...
Side 2 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.