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 sider |
Fra bogen
Resultater 1-5 af 16
Side 112
... tiple of the fourth ; then the first is said to have to the second a greater ratio than the third magnitude has to the fourth ; and on the contrary , the third is faid to have to the fourth a less ratio than the first has to the second ...
... tiple of the fourth ; then the first is said to have to the second a greater ratio than the third magnitude has to the fourth ; and on the contrary , the third is faid to have to the fourth a less ratio than the first has to the second ...
Side 115
... tiple of another , is greater than that other magnitude . IF PROP . I. THEOR . Fany number of magnitudes be equimultiples of as many , each of each ; what multiple foever any one of them is of its part , the fame multiple shall all the ...
... tiple of another , is greater than that other magnitude . IF PROP . I. THEOR . Fany number of magnitudes be equimultiples of as many , each of each ; what multiple foever any one of them is of its part , the fame multiple shall all the ...
Side 118
... tiple of A , that Lis of C. for the fame reason M is the same multiple of B , that N is of D. and because KE ABGM LFCDHN : b . Hypoth . as A is to B , so is C to Db , and of A and C have been taken certain e- quimultiples K , L ; and of ...
... tiple of A , that Lis of C. for the fame reason M is the same multiple of B , that N is of D. and because KE ABGM LFCDHN : b . Hypoth . as A is to B , so is C to Db , and of A and C have been taken certain e- quimultiples K , L ; and of ...
Side 119
... tiple of the remainder FD , that the whole AB is of the whole CD . G A Take AG the fame multiple of FD , that AE is of CF. therefore AE is the fame multiple of CF , that EG is of CD . but AE , by the hypothe- sis , is the fame multiple ...
... tiple of the remainder FD , that the whole AB is of the whole CD . G A Take AG the fame multiple of FD , that AE is of CF. therefore AE is the fame multiple of CF , that EG is of CD . but AE , by the hypothe- sis , is the fame multiple ...
Side 120
... tiple of FD , that AB is of CD . Therefore if one magnitude , & c . Q. E. D. See N. PROP . VI . THEOR . IF two magnitudes be equimultiples of two others , and if equimultiples of these be taken from the first two , the remainders are ...
... tiple of FD , that AB is of CD . Therefore if one magnitude , & c . Q. E. D. See N. PROP . VI . THEOR . IF two magnitudes be equimultiples of two others , and if equimultiples of these be taken from the first two , the remainders are ...
Andre udgaver - Se alle
Almindelige termer og sætninger
alfo alſo angle ABC angle BAC bafe baſe BC is equal BC is given becauſe the angle becauſe the ratio biſected Book XI cafe cauſe circle ABCD circumference cone conſtruction cylinder demonftrated deſcribed diameter drawn equal angles equiangular equimultiples Euclid exceſs fame multiple fame ratio fame reaſon fides fimilar firſt folid angle 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 likewife oppoſite parallel parallelepipeds parallelogram perpendicular priſms Propofition proportionals pyramid Q. E. D. PROP rectangle rectangle contained rectilineal figure right angles ſame ſecond ſegment ſhall ſhewn ſide ſpace ſphere ſquare of AC ſtraight line AB ſtraight line BC THEOR theſe thoſe tiple triangle ABC vertex wherefore
Populære passager
Side 5 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 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.
Side 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.
Side 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...
Side 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...
Side 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.
Side 167 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Side 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.
Side 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.
Side 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.