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 9
... contained by those fides equal to one another ; their bafes shall like- wife be equal , and the triangles be equal , and their other angles to which the equal fides are oppofite , fhall be equal , each to each . Which was to be ...
... contained by those fides equal to one another ; their bafes shall like- wife be equal , and the triangles be equal , and their other angles to which the equal fides are oppofite , fhall be equal , each to each . Which was to be ...
Página 12
... contained by the two fides of the one shall be equal to the angle contained by the two fides equal to them , of the other . A DG Let ABC , DEF be two triangles having the two fides AB , AC e- qual to the two fides DE , DF , each to each ...
... contained by the two fides of the one shall be equal to the angle contained by the two fides equal to them , of the other . A DG Let ABC , DEF be two triangles having the two fides AB , AC e- qual to the two fides DE , DF , each to each ...
Página 22
... contained by the two fides equal to them , of the o- ther ; the bafe of that which has the greater angle shall be greater than the bafe of the other . Let ABC , DEF be two triangles which have the two fides AB , AC AC equal to the two ...
... contained by the two fides equal to them , of the o- ther ; the bafe of that which has the greater angle shall be greater than the bafe of the other . Let ABC , DEF be two triangles which have the two fides AB , AC AC equal to the two ...
Página 23
... contained by the fides equal to them , of the other . Let ABC , DEF be two triangles which have the two fides AB , AC equal to the two fides DE , DF , each to each , viz . AB equal to DE , and AC to DF ; but the bafe CB greater than the ...
... contained by the fides equal to them , of the other . Let ABC , DEF be two triangles which have the two fides AB , AC equal to the two fides DE , DF , each to each , viz . AB equal to DE , and AC to DF ; but the bafe CB greater than the ...
Página 41
... angle , be equal to the fquares described upon the o- ther two fides of it ; the angle contained by these two fides is a right angle . Book I. * . II . I. If the fquare If OF 41 EUCLID . GB, HC; and thro' A draw b ...
... angle , be equal to the fquares described upon the o- ther two fides of it ; the angle contained by these two fides is a right angle . Book I. * . II . I. If the fquare If OF 41 EUCLID . GB, HC; and thro' A draw b ...
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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.