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, The Book of Euclid's Data, in Like Manner Corrected. viz. The first six books, together with the eleventh and twelfthA. Foulis, 1781 - 466 σελίδες |
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Σελίδα 388
... given . but as LM to MN , fo is GH to HK ; wherefore the ra- tio of GH to HK is given . 39 . See N. 2. 22. I. IF PROP . XLII . each of the fides of a triangle be given in magni- tude ; the triangle is given in species . Let each of the ...
... given . but as LM to MN , fo is GH to HK ; wherefore the ra- tio of GH to HK is given . 39 . See N. 2. 22. I. IF PROP . XLII . each of the fides of a triangle be given in magni- tude ; the triangle is given in species . Let each of the ...
Σελίδα 397
... given in fpecies , a straight line be drawn to the base in a given angle ; it fhall have a given ratio to the base ... species . Let the rectilineal figure ABCDE be given in fpecies ; ABCDE may be divided into triangles given in fpecies ...
... given in fpecies , a straight line be drawn to the base in a given angle ; it fhall have a given ratio to the base ... species . Let the rectilineal figure ABCDE be given in fpecies ; ABCDE may be divided into triangles given in fpecies ...
Σελίδα 398
... given in species be deferibed the fame ftraight line ; they fhall have a given ra- tio to one another . Let the triangles ABC , ABD given in fpecies be defcribed upcr the fame ftraight line AB ; the ratio of the triangle ABC to the ...
... given in species be deferibed the fame ftraight line ; they fhall have a given ra- tio to one another . Let the triangles ABC , ABD given in fpecies be defcribed upcr the fame ftraight line AB ; the ratio of the triangle ABC to the ...
Σελίδα 405
... species . and because pon the given ftraight line C the figure D given in Decies is defcribed , Dis Iven in magnitu le , and E A D L F B H M K b . 56. Dat . ae figure A is given in magnitude , therefore the ratio of A to D given . and ...
... species . and because pon the given ftraight line C the figure D given in Decies is defcribed , Dis Iven in magnitu le , and E A D L F B H M K b . 56. Dat . ae figure A is given in magnitude , therefore the ratio of A to D given . and ...
Σελίδα 424
... given , and if the ratio of the rectangle of the fides which contain the given angle to the fquare of the third fide be given ; the tri- angle is given in species . Let the triangle ABC have the given angle BAC , and let the ratio of ...
... given , and if the ratio of the rectangle of the fides which contain the given angle to the fquare of the third fide be given ; the tri- angle is given in species . Let the triangle ABC have the given angle BAC , and let the ratio of ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
AC is equal alfo alſo angle ABC angle BAC bafe baſe BC is given becauſe the angle bifected Book XI cafe circle ABCD circumference cone confequently cylinder defcribed demonftrated diameter drawn EFGH equal angles equiangular equimultiples Euclid excefs faid fame manner fame multiple fame ratio fecond fegment fhall fhewn fide BC fides fimilar fince firft firſt folid angle fome fore fquare of AC ftraight line AB given angle given ftraight line given in fpecies given in magnitude given in pofition given magnitude given ratio gnomon greater join lefs leſs likewife line BC muſt oppofite parallel parallelepipeds parallelogram perpendicular prifm Propofition proportionals pyramid rectangle contained rectilineal figure right angles ſhall ſphere ſquare thefe THEOR theſe thro tiple triangle ABC vertex wherefore
Δημοφιλή αποσπάσματα
Σελίδα 156 - 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.
Σελίδα 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.
Σελίδα 323 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Σελίδα 92 - If from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it ; if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, be equal to the square- of the line which meets it, the line which meets shall touch the circle.
Σελίδα 80 - EA : and because AD is equal to DC, and DE common to the triangles ADE, CDE, the two sides AD, DE are equal to the two CD, DE, each to each ; and the angle ADE is equal to the angle CDE, for each of them is a right angle ; therefore the base AE is equal (4.
Σελίδα 52 - If a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double of the square of half the line bisected, and of the square of the line made up of the half and the part produced.
Σελίδα 36 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Σελίδα 2 - 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.
Σελίδα 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.
Σελίδα 74 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...