The Elements of Euclid: Viz. the First Six Books, with the Eleventh and Twelfth. In which the Corrections of Dr. Simson are Generally Adopted, But the Errors Overlooked by Him are Corrected, and the Obscurities of His and Other Editions Explained. Also Some of Euclid's Demonstrations are Restored, Others Made Shorter and More General, and Several Useful Propositions are Added. Together with Elements of Plane and Spherical Trigonometry, and a Treatise on Practical GeometryJ. Pillans & sons, 1799 - 351 páginas |
Dentro del libro
Resultados 1-5 de 13
Página 110
... second , so many times does the fame multiple of the third contain the fourth . VI . Magnitudes which have the same ratio , are called Proportionals . N. B. When four magnitudes are proportionals , it is ufually expreffed by faying ...
... second , so many times does the fame multiple of the third contain the fourth . VI . Magnitudes which have the same ratio , are called Proportionals . N. B. When four magnitudes are proportionals , it is ufually expreffed by faying ...
Página 111
... second ; and fo on , quadruplicate , & c . increasing the denomination ftill by unity . F. In any number of ... second is to the first as the fourth to the third . Prop . B. Book V. XV . By Compofition , it is inferred , that the first ...
... second ; and fo on , quadruplicate , & c . increasing the denomination ftill by unity . F. In any number of ... second is to the first as the fourth to the third . Prop . B. Book V. XV . By Compofition , it is inferred , that the first ...
Página 112
... second of the first rank , as the laft but one to the last of the other rank ; and the second to the third , as the last but two to the last but one ; and so on ; then it is inferred , by perturbate equality , that the first is to the ...
... second of the first rank , as the laft but one to the last of the other rank ; and the second to the third , as the last but two to the last but one ; and so on ; then it is inferred , by perturbate equality , that the first is to the ...
Página 116
... second , as the fame multiple of the third to the fourth and in like manner , the first is to any multiple of the fecond , as the third to the fame multiple of the fourth . For , it was proved in the propofition , that as many times as ...
... second , as the fame multiple of the third to the fourth and in like manner , the first is to any multiple of the fecond , as the third to the fame multiple of the fourth . For , it was proved in the propofition , that as many times as ...
Página 122
... second , than the third has to the fourth , but the third the fame ratio to the fourth , which the fifth has to the fixth ; it may be demon- ftrated in like manner , that the firft has a greater ratio to the fecond , than the fifth has ...
... second , than the third has to the fourth , but the third the fame ratio to the fourth , which the fifth has to the fixth ; it may be demon- ftrated in like manner , that the firft has a greater ratio to the fecond , than the fifth has ...
Términos y frases comunes
ABC is equal ABCD alfo alſo angle ABC angle ACB angle BAC arch bafe baſe becauſe the angle bifect Book XI cafe centre circle ABC circumference cofine confequently cylinder defcribed demonftrated diameter equal angles equiangular equimultiples Euclid exterior angle faid fame altitude fame manner fame multiple fame number fame ratio fame reaſon fecond fegment fhall fides fimilar firft firſt folid angle fome fore fquare fquare of AC fuperficies given ftraight line gnomon greater half the fum join lefs leſs Let ABC magnitudes meaſure oppofite angle pafs parallel parallelogram parallelopiped perpendicular plane angles prifm PROB propofition proportionals Q. E. D. PROP radius rectangle contained rectilineal figure remaining angle right angles ſhall ſquare tangent thefe THEOR theſe tiple triangle ABC Wherefore
Pasajes populares
Página 30 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Página 142 - 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 13 - Let it be granted that a straight line may be drawn from any one point to any other point.
Página 30 - ... then shall the other sides be equal, each to each; and also the third angle of the one to the third angle of the other. Let ABC, DEF be two triangles which have the angles ABC, BCA equal to the angles DEF, EFD, viz.
Página 72 - 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...
Página 57 - 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...
Página 145 - AC the same multiple of AD, that AB is of the part which is to be cut off from it : join BC, and draw DE parallel to it : then AE is the part required to be cut off.
Página 48 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Página 35 - F, which is the common vertex of the triangles ; that is, together with four right angles. 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 10 - 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.