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 Seiten |
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Seite 23
... pass through either extremity of the base . In this case it follows immediately ( V ) that the angles A B C and A G C are equal ; for the lines BC and CG must coincide with BG , since each has two points upon it ( 52 ) . Hence in every ...
... pass through either extremity of the base . In this case it follows immediately ( V ) that the angles A B C and A G C are equal ; for the lines BC and CG must coincide with BG , since each has two points upon it ( 52 ) . Hence in every ...
Seite 23
... pass through either extremity of the base . In this case it follows immediately ( V ) that the angles A B C and A G C are equal ; for the lines BC and C G must coincide with BG , since each has two points upon it ( 52 ) . Hence in every ...
... pass through either extremity of the base . In this case it follows immediately ( V ) that the angles A B C and A G C are equal ; for the lines BC and C G must coincide with BG , since each has two points upon it ( 52 ) . Hence in every ...
Seite 43
... pass through the same point . This is , in fact , equivalent to the twelfth axiom ( 115 ) . PROPOSITION XXXI . PROBLEM . ( 123 ) Through a given point ( C ) to draw a right line parallel to a given right line ( A B ) . Solution . D с R ...
... pass through the same point . This is , in fact , equivalent to the twelfth axiom ( 115 ) . PROPOSITION XXXI . PROBLEM . ( 123 ) Through a given point ( C ) to draw a right line parallel to a given right line ( A B ) . Solution . D с R ...
Seite 54
... pass through the same point . D ( 181 ) COR . 8. - The lines which join the middle points DEF of the three sides of a triangle divide it into four triangles which are equal in every respect . ( 182 ) COR . 9. - The line joining the ...
... pass through the same point . D ( 181 ) COR . 8. - The lines which join the middle points DEF of the three sides of a triangle divide it into four triangles which are equal in every respect . ( 182 ) COR . 9. - The line joining the ...
Seite 91
... pass through the centre . If parts be taken upon it in both directions from the centre greater than the radius , their extremities will be without the circle ( 22 ) , and if parts be taken on it in both directions from the centre less ...
... pass through the centre . If parts be taken upon it in both directions from the centre greater than the radius , their extremities will be without the circle ( 22 ) , and if parts be taken on it in both directions from the centre less ...
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The First Six Books of the Elements of Euclid: With a Commentary and ... Dionysius Lardner Keine Leseprobe verfügbar - 2018 |
Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 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.
Seite 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.
Seite 22 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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...
Seite 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...
Seite 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...