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 twelfth |
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Page 36
... BC , and between the fame parallels BC , AE ; the paral- lelogram ABCD is double of the tri- angle EBC . Join AC ... given triangle , and have one of its angles equal to a given rectilineal angle . Let ABC be the given triangle , and D ...
... BC , and between the fame parallels BC , AE ; the paral- lelogram ABCD is double of the tri- angle EBC . Join AC ... given triangle , and have one of its angles equal to a given rectilineal angle . Let ABC be the given triangle , and D ...
Page 40
... given straight line . Let AB be the given straight line ; it is required to describe a fquare upon AB . a From the ... BC , is equal to the fquares de- fcribed upon BA , AC . a On BC defcribe the fquare BDEC , and on BA , AC the squares ...
... given straight line . Let AB be the given straight line ; it is required to describe a fquare upon AB . a From the ... BC , is equal to the fquares de- fcribed upon BA , AC . a On BC defcribe the fquare BDEC , and on BA , AC the squares ...
Page 57
... BC are equal to the fquare of AC , and twice the fquare of Book II . BC , and twice the rectangle BC , CD . but ... given See N. rectilineal figure . Let A be the given rectilineal figure ; it is required to describe a fquare that shall ...
... BC are equal to the fquare of AC , and twice the fquare of Book II . BC , and twice the rectangle BC , CD . but ... given See N. rectilineal figure . Let A be the given rectilineal figure ; it is required to describe a fquare that shall ...
Page 84
... BC is equal to the bafe EF . Therefore in equal circles , & c . Q. E. D. 4. 10. 1 . PRO P. XXX . PRO B. To bifect a given circumference , that is to divide it into two equal parts . Let ADB be the given circumference ; it is required to ...
... BC is equal to the bafe EF . Therefore in equal circles , & c . Q. E. D. 4. 10. 1 . PRO P. XXX . PRO B. To bifect a given circumference , that is to divide it into two equal parts . Let ADB be the given circumference ; it is required to ...
Page 88
... given ftraight line AB the fegment G E D AHB of a circle is defcribed which ... BC is D drawn from the point of contact B , the angle FBC is c t . 32. 3 ... given circle ABC containing an angle equal to the given angle D. which was to be ...
... given ftraight line AB the fegment G E D AHB of a circle is defcribed which ... BC is D drawn from the point of contact B , the angle FBC is c t . 32. 3 ... given circle ABC containing an angle equal to the given angle D. which was to be ...
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Common terms and phrases
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
Popular passages
Page 5 - Let it be granted that a straight line may be drawn from any one point to any other point.
Page 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.
Page 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.
Page 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...
Page 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...
Page 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.
Page 167 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Page 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.
Page 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.
Page 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.