The Elements of Euclid: The Errors by which Theon, Or Others, Have Long Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also the Book of Euclid's Data, in Like Manner Corrected. viz. the first six books, together with the eleventh and twelfthJ. Collingwood, 1827 - 513 páginas |
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Página ix
... proportion of plane figures ; the 7th , 8th , and 9th , give us the funda- mental properties of numbers ; the 10th contains the theory of commensurable and incommensurable lines and spaces ; the 11th , 12th , 13th , 14th and 15th SHORT ...
... proportion of plane figures ; the 7th , 8th , and 9th , give us the funda- mental properties of numbers ; the 10th contains the theory of commensurable and incommensurable lines and spaces ; the 11th , 12th , 13th , 14th and 15th SHORT ...
Página 102
... proportion is the similitude of ratios . ” IX . Proportion consists in three terms at least . X. When three magnitudes are proportionals , the first is said to have to the third the duplicate ratio of that which it has to the second ...
... proportion is the similitude of ratios . ” IX . Proportion consists in three terms at least . X. When three magnitudes are proportionals , the first is said to have to the third the duplicate ratio of that which it has to the second ...
Página 105
... proportion . It is demonstrated in the 22d Prop . Book 5 . XX . Ex æquali in proportione perturbatâ seu inordinatâ , from equality in perturbate or disorderly proportion * . This term is used when the first magnitude is to the second of ...
... proportion . It is demonstrated in the 22d Prop . Book 5 . XX . Ex æquali in proportione perturbatâ seu inordinatâ , from equality in perturbate or disorderly proportion * . This term is used when the first magnitude is to the second of ...
Página 155
... figure A shall be similar to the figure B. Because A is similar to C , they are equiangular , and also have their sides about the equal angles proportion- 11.5 . Cor.19.6 . * 1 Def . 6. al * : again , BOOK VI . PROP . XXI . 155.
... figure A shall be similar to the figure B. Because A is similar to C , they are equiangular , and also have their sides about the equal angles proportion- 11.5 . Cor.19.6 . * 1 Def . 6. al * : again , BOOK VI . PROP . XXI . 155.
Página 280
... proportion of num- " bers to one another is defined , and treated of , yet " without giving any definition of the ratio of numbers ; " though such a definition was as necessary and useful " to be given in that book as in this : but ...
... proportion of num- " bers to one another is defined , and treated of , yet " without giving any definition of the ratio of numbers ; " though such a definition was as necessary and useful " to be given in that book as in this : but ...
Outras edições - Ver tudo
The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ... Robert Simson Visualização integral - 1775 |
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Robert Simson Visualização integral - 1762 |
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Robert Simson Visualização integral - 1781 |
Palavras e frases frequentes
ABC is given AC is equal altitude angle ABC angle BAC base BC bisected centre circle ABCD circumference common logarithm cone Constr cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC logarithm multiple parallel parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle contained rectilineal figure right angles ROBERT SIMSON segment shewn sides BA similar sine solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR triangle ABC vertex wherefore
Passagens conhecidas
Página 141 - 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 40 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let...
Página 26 - If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another, and the exterior angle equal to the interior and opposite upon the same side, and also the two interior angles upon the same side together equal to two right angles.
Página 46 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Página 28 - Cor. angles; that is * together with four right angles. There1s, 1. fore 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 21 - If two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other.
Página 12 - IF two triangles have two sides of the one equal to two sides of the other, each to each, and have likewise their bases equal; the angle. which is contained by the two sides...
Página 169 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Página 5 - LET it be granted that a straight line may be drawn from any one point to any other point. 2. That a terminated straight line may be produced to any length in a straight line. 3. And that a circle may be described from any centre, at any distance from that centre.
Página 97 - 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.