The Elements of geometry; or, The first six books, with the eleventh and twelfth, of Euclid, with corrections, annotations, and exercises, by R. Wallace. Cassell's edCassell, Petter and Galpin, 1881 - 212 sider |
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Side 6
... Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one another . IX . The whole is greater than its part Dr. Thomson , in his edition of Euclid , has added to this axiom , another ...
... Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one another . IX . The whole is greater than its part Dr. Thomson , in his edition of Euclid , has added to this axiom , another ...
Side 48
... magnitudes . Therefore the square of CD and twice the rectangle A C. CD are together equal to four times the rectangle A B. B C. To these equals add the square of A C. Therefore the squares of AC and CD , and twice the rectangle AC ...
... magnitudes . Therefore the square of CD and twice the rectangle A C. CD are together equal to four times the rectangle A B. B C. To these equals add the square of A C. Therefore the squares of AC and CD , and twice the rectangle AC ...
Side 55
... , that point is within the circle ; and if a point be taken beyond the circumference , it is without the circle . This axiom is tacitly assumed by Euclid in this Book , II . if two magnitudes be doubles of two other BOOK III . AXIOMS . 65.
... , that point is within the circle ; and if a point be taken beyond the circumference , it is without the circle . This axiom is tacitly assumed by Euclid in this Book , II . if two magnitudes be doubles of two other BOOK III . AXIOMS . 65.
Side 56
Euclides Robert Wallace. II . if two magnitudes be doubles of two other magnitudes , each of cach , the sum of the first two is double the sum of the other two . III . If two magnitudes be doubles of two other magnitudes , each of each ...
Euclides Robert Wallace. II . if two magnitudes be doubles of two other magnitudes , each of cach , the sum of the first two is double the sum of the other two . III . If two magnitudes be doubles of two other magnitudes , each of each ...
Side 97
... Magnitudes are said to have a ratio to one another , when the less can be multiplied so as to exceed the other . This definition is intended as a test of the likeness or similarity of any two magnitudes ; for unless the one can be ...
... Magnitudes are said to have a ratio to one another , when the less can be multiplied so as to exceed the other . This definition is intended as a test of the likeness or similarity of any two magnitudes ; for unless the one can be ...
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The Elements of geometry; or, The first six books, with the eleventh and ... Euclides Uten tilgangsbegrensning - 1855 |
The Elements of Geometry: Or, the First Six Books, with the Eleventh and ... Euclides Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
A B and CD AC is equal adjacent angles altitude angle ABC angle ACB angle BAC angle EDF angle equal base BC bisected centre circle ABCD circumference common section cone Corollary cylinder described diameter draw equal angles equal Ax equal Const equal Hyp equiangular equimultiples Euclid exterior angle fore given rectilineal given straight line gnomon homologous inscribed join less Let the straight meet multiple opposite angle parallel parallelogram parallelopiped pentagon perpendicular polygon prism produced proposition Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment solid angle solid CD sphere squares of AC straight line drawn straight lines A B THEOREM third three plane angles three straight lines touches the circle triangle ABC triplicate ratio twice the rectangle vertex Wherefore
Populære avsnitt
Side 21 - 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.
Side 41 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Side 2 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.
Side 93 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...
Side 25 - 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 126 - 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 93 - A LESS magnitude is said to be a part of a greater magnitude, when the less measures the greater, that is, ' when the less is contained a certain number of times exactly in the greater.
Side 40 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Side 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.
Side 19 - THEOREM. IF two triangles have two sides of the one equal to two sides of the...