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 páginas |
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Página 112
... proportionals . N. B. When four magnitudes are proportionals , it is usually ' expressed by saying , the first is to the second , as the third to * the fourth . ' VII . When of the equimultiples of four magnitudes ( taken as in the 5th ...
... proportionals . N. B. When four magnitudes are proportionals , it is usually ' expressed by saying , the first is to the second , as the third to * the fourth . ' VII . When of the equimultiples of four magnitudes ( taken as in the 5th ...
Página 113
... proportionals . " ΧΙΙΙ . Permutando , or Alternando , by Permutation , or alternately ; this word is ufed when there are four proportionals , and it is infer- Sce N. red , that the first has the fame ratio to the third , which the se ...
... proportionals . " ΧΙΙΙ . Permutando , or Alternando , by Permutation , or alternately ; this word is ufed when there are four proportionals , and it is infer- Sce N. red , that the first has the fame ratio to the third , which the se ...
Página 114
... proportionals when taken two and two of each rank , and it is inferred , that the first is to the last of the first rank of magnitudes , as the first is to the laft of the others . ' of this there are the two following kinds , which ...
... proportionals when taken two and two of each rank , and it is inferred , that the first is to the last of the first rank of magnitudes , as the first is to the laft of the others . ' of this there are the two following kinds , which ...
Página 121
... proportionals , they portionals also when taken inversely . are pro- Sce N. If the magnitude A be to B , as C is to D , then also inversely B is to A , as D to C. Take of B and D any equimultiples what- ever E and F ; and of A and C any ...
... proportionals , they portionals also when taken inversely . are pro- Sce N. If the magnitude A be to B , as C is to D , then also inversely B is to A , as D to C. Take of B and D any equimultiples what- ever E and F ; and of A and C any ...
Página 128
... proportionals , as one of the antecedents is to its confequent , so shall all the antecedents taken together be to all the confe- quents . Let any number of magnitudes A , B , C , D , E , F , be propor tionals ; that is , as A is to B ...
... proportionals , as one of the antecedents is to its confequent , so shall all the antecedents taken together be to all the confe- quents . Let any number of magnitudes A , B , C , D , E , F , be propor tionals ; that is , as A is to B ...
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Términos y frases comunes
AC is equal alfo alſo angle ABC angle BAC bafe baſe BC is given becauſe the angle biſected Book XI cafe cauſe circle ABCD circumference cone conſtruction cylinder demonftrated deſcribed diameter drawn EFGH equal angles equiangular equimultiples Euclid exceſs faid fame multiple fame ratio fame reaſon fegment 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 line BC oppoſite parallel parallelepipeds parallelogram paſs perpendicular proportionals Propoſition pyramid Q. E. D. PROP rectangle contained rectilineal figure right angles ſame ſecond ſhall ſhall be equal ſhewn ſide ſpace ſphere ſquare of AC ſtraight line AC THEOR theſe thoſe thro tiple triangle ABC vertex wherefore
Pasajes populares
Página 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.
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 323 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
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 74 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...