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 páginas |
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Página xiii
... called triangles are considered . In attempting this , it is curious to observe the difficulties into which these authors fall , and the expedients to which they are compelled to resort . Some find it necessary to prove that every point ...
... called triangles are considered . In attempting this , it is curious to observe the difficulties into which these authors fall , and the expedients to which they are compelled to resort . Some find it necessary to prove that every point ...
Página xiv
... called Euclid's postulate , and those which relate to his doctrine of proportion . On the former , I have enlarged so fully in Appendix II . that little remains to be said here . I have there shown that what is really assumed by Euclid ...
... called Euclid's postulate , and those which relate to his doctrine of proportion . On the former , I have enlarged so fully in Appendix II . that little remains to be said here . I have there shown that what is really assumed by Euclid ...
Página 2
... called a line , right or curved , as the case may be . This , however , cannot , in the strict geometrical sense of the term , be a line at all , since it has breadth as well as length ; for if it had not it could not be made evident to ...
... called a line , right or curved , as the case may be . This , however , cannot , in the strict geometrical sense of the term , be a line at all , since it has breadth as well as length ; for if it had not it could not be made evident to ...
Página 3
... called abstraction . If a perfectly flexible string be pulled by its extremities in opposite directions , it will ... called a curve . Every surface which is not a plane , or composed of planes , is called a curved surface . ( 9 ) VIII ...
... called abstraction . If a perfectly flexible string be pulled by its extremities in opposite directions , it will ... called a curve . Every surface which is not a plane , or composed of planes , is called a curved surface . ( 9 ) VIII ...
Página 4
... called a right angle , and each of these lines is said to be perpendicular to the other . ( 12 ) XI . An obtuse angle is an angle greater than a right angle . ( 13 ) XII . An acute angle is an angle less than a right angle . کے ( 14 ) ...
... called a right angle , and each of these lines is said to be perpendicular to the other . ( 12 ) XI . An obtuse angle is an angle greater than a right angle . ( 13 ) XII . An acute angle is an angle less than a right angle . کے ( 14 ) ...
Otras ediciones - Ver todas
The First Six Books of the Elements of Euclid: With a Commentary and ... Dionysius Lardner Sin vista previa disponible - 2018 |
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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.
Página 22 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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...
Página 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...
Página 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...