The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected and Some of Euclid's Demonstrations are Restored. Also, to this Second Edition is Added the Book of Euclid's Data. In Like Manner Corrected. viz. the first six books, together with the eleventh and twelfthR. and A. Foulis, 1762 - 466 páginas |
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Página 167
... given straight line fimilar to one given , and so on . Which was to be done . e . 1 , Def . 6 . C. 4. 6 . d . 22. 5 , SIMILAR PROP . XIX . THEOR . IMILAR triangles are to one another in the duplicate ratio of their homologous fides ...
... given straight line fimilar to one given , and so on . Which was to be done . e . 1 , Def . 6 . C. 4. 6 . d . 22. 5 , SIMILAR PROP . XIX . THEOR . IMILAR triangles are to one another in the duplicate ratio of their homologous fides ...
Página 180
... given straight line AB which shall be` equal to the figure C , exceeding by a parallelogram similar to D. C. 21. 6 ... ratio . Let AB be the given straight line ; it is required to cut it in ex- frome and mean ratio , Upon a Upon AB ...
... given straight line AB which shall be` equal to the figure C , exceeding by a parallelogram similar to D. C. 21. 6 ... ratio . Let AB be the given straight line ; it is required to cut it in ex- frome and mean ratio , Upon a Upon AB ...
Página 304
... given angle , tho ' there neither is , nor can be any thing in the Pro- pofition relating to a given angle . PROP ... ratio to beginners , by premising this Metaphysical Defi- " nition , to the more accurate Definitions of ratios that ...
... given angle , tho ' there neither is , nor can be any thing in the Pro- pofition relating to a given angle . PROP ... ratio to beginners , by premising this Metaphysical Defi- " nition , to the more accurate Definitions of ratios that ...
Página 305
... proportion of numbers to one another is defined , and treated of , yet without giving any Definition of the ratio of numbers ; tho ' fuch a Definition was as neceffary and use- " ful to be given in that Book , as in this . but indeed ...
... proportion of numbers to one another is defined , and treated of , yet without giving any Definition of the ratio of numbers ; tho ' fuch a Definition was as neceffary and use- " ful to be given in that Book , as in this . but indeed ...
Página 312
... ratio that B has to C , then if any equimultiples whatever of A and B be ... given the demonftration of the 10. Propofition as we now have it , inflead ... ratio , are the fame to one another ; but explicitely demonftrates this in Prop ...
... ratio that B has to C , then if any equimultiples whatever of A and B be ... given the demonftration of the 10. Propofition as we now have it , inflead ... ratio , are the fame to one another ; but explicitely demonftrates this in Prop ...
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Términos y frases comunes
alfo alſo angle ABC angle BAC bafe baſe BC is equal BC is given becauſe the angle becauſe the ratio bifected Book XI cafe circle ABCD circumference cone confequently conftruction cylinder defcribed demonftrated drawn equal angles equiangular equimultiples Euclid excefs faid fame multiple fame ratio fame reaſon fecond fegment fhall fhewn fides fimilar firft firſt folid angle fome fore fquare of BC given angle given in fpecies given in magnitude given in pofition given magnitude given ratio given ſtraight line gnomon greater join lefs leſs Let ABC likewife line BC muſt oppofite parallel parallelepipeds parallelogram perpendicular polygon prifms Propofition proportionals pyramid Q. E. D. PROP reafon rectangle rectangle contained rectilineal figure right angles ſhall ſphere ſquare ſtraight line AB thefe THEOR theſe thro tiple triangle ABC wherefore
Pasajes populares
Página 5 - Let it be granted that a straight line may be drawn from any one point to any other point.
Página 163 - 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 48 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square of AC.
Página 73 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle; and no straight line can be drawn from the extremity between that straight line and the circumference, so as not to cut the circle...
Página 105 - 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...
Página 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.
Página 167 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Página 54 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Página 47 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Página 37 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.