The First Six Books of the Elements of Euclid, with a Commentary and Geometrical Exercises: To which are Annexed a Treatise on Solid Geometry, and a Short Essay on the Ancient Geometrical AnalysisJohn Taylor, 30 Upper Gower Street, Bookseller and Publisher to the University: and sold, 1828 - 324 sider |
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Resultat 1-5 av 47
Side 11
... doubles of the same or equal magnitudes are equal . ( 49 ) VII . The halves of the same or equal magnitudes are equal . £ VIII . Magnitudes which coincide with one another , or exactly fill the same space , are equal . ( 50 ) ( 51 ) IX ...
... doubles of the same or equal magnitudes are equal . ( 49 ) VII . The halves of the same or equal magnitudes are equal . £ VIII . Magnitudes which coincide with one another , or exactly fill the same space , are equal . ( 50 ) ( 51 ) IX ...
Side 50
... doubles , the parallelo- grams , are equal . ( 163 ) Hence the squares of equal lines are equal . ( 164 ) Also equal squares have equal sides . For the diagonals being drawn , the right angled isosceles triangles into which they divide ...
... doubles , the parallelo- grams , are equal . ( 163 ) Hence the squares of equal lines are equal . ( 164 ) Also equal squares have equal sides . For the diagonals being drawn , the right angled isosceles triangles into which they divide ...
Side 53
... double the base of the other , the area of the one will be also double the area of the other . Also if they have equal bases and the altitude of one be double the altitude of the other , the area of the one will be double the area of ...
... double the base of the other , the area of the one will be also double the area of the other . Also if they have equal bases and the altitude of one be double the altitude of the other , the area of the one will be double the area of ...
Side 55
... double of the triangle BAC ( XXXIV ) , therefore BD is also double of the triangle B E C. B DE ( 191 ) This proposition may be generalized thus : If a parallelogram and triangle have equal bases and altitudes , the parallelogram is ...
... double of the triangle BAC ( XXXIV ) , therefore BD is also double of the triangle B E C. B DE ( 191 ) This proposition may be generalized thus : If a parallelogram and triangle have equal bases and altitudes , the parallelogram is ...
Side 59
... double of the triangle ICA , as they are upon the same base CI , and between the same parallels ( XLI ) ; and the parallelogram CE is double of the triangle BCF , as they are upon the same base CF , and between the same parallels ( XLI ) ...
... double of the triangle ICA , as they are upon the same base CI , and between the same parallels ( XLI ) ; and the parallelogram CE is double of the triangle BCF , as they are upon the same base CF , and between the same parallels ( XLI ) ...
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The First Six Books of the Elements of Euclid, with a Commentary and ... Euclid,Dionysius Lardner Uten tilgangsbegrensning - 1851 |
The First Six Books of the Elements of Euclid, with a Commentary and ... Euclid,Dionysius Lardner Uten tilgangsbegrensning - 1855 |
The First Six Books of the Elements of Euclid: With a Commentary and ... Dionysius Lardner Ingen forhåndsvisning tilgjengelig - 2018 |
Vanlige uttrykk og setninger
A B and B C A B D altitude angles A B C arcs Book centre circumference circumscribed coincide conical surface constructed demonstration diagonal diameter difference draw equal angles equal hyp equal sides equi equiangular equilateral triangle equimultiples Euclid external angle extremities geometry given circle given line given point given right line Hence homologous sides hypotenuse inscribed intersect isosceles triangle less magnitudes multiple opposite parallel parallelogram parallelopiped pentagon perpendicular plane polygon prism problem produced PROPOSITION proved pyramid radii radius rectangle rectilinear figure respectively equal right line A B segments sides A B similar solid angle square of A B surface tangent THEOREM third tiples triangles A B C vertex
Populære avsnitt
Side 16 - If two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles supplemental, the two triangles are equal.
Side 24 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Side 22 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Side 104 - ... be equimultiples, the one of the second, and the other of the fourth. Let A the first be the same multiple of B the second, that C the third is of D the fourth ; and of A, C let equimultiples EF, GH be taken.
Side 107 - ... If there be three magnitudes, and other three, which have the same ratio taken two and two, but in a cross order; then if the first magnitude be greater than the third, the fourth shall be greater than the sixth: and if equal, equal; and if less, less.
Side 107 - N ; and if equal, equal ; and if less, less : but if G be greater than L, it has been shown that L HC K E M F N H is greater than M ; and if equal, equal; and if less, less: therefore, if G be greater than L, K is greater than N ; and if equal, equal ; and if less less : and G, K are any equimultiples whatever of A, E ; and L, N any whatever of B, F : therefore as A is to B, so is E to F (5.
Side 187 - If two angles of one triangle are equal to two angles of another triangle, the third angles are equal, and the triangles are mutually equiangular.
Side 107 - IF the first be to the second as the third to the fourth, and if the first be a multiple, or part of the second; the third is the same multiple, or the same part of the fourth...
Side 107 - THEOR. IF the first be the same multiple of the second, or the same part of it, that the third is of the fourth ; the first is to the second, as the third is to the fourth...
Side 107 - D (as in fig. 2 and 3), this magnitude can be multiplied, so as to become greater than D, whether it be AC, or CB. Let it be multiplied until it...