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 Seiten |
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Seite 98
... proportionals . N.B. " When four magnitudes are proportionals , this property is usually expressed by saying , the first is to the second , as the third to the fourth . " This definition merely explains the term proportional as applied ...
... proportionals . N.B. " When four magnitudes are proportionals , this property is usually expressed by saying , the first is to the second , as the third to the fourth . " This definition merely explains the term proportional as applied ...
Seite 99
... proportionals , the first is said to have to the fourth , the triplicate ratio of that which it has to the second , and so on ; quadruplicate , & c . , increasing the denomination still by unity in any number of proportionals . When ...
... proportionals , the first is said to have to the fourth , the triplicate ratio of that which it has to the second , and so on ; quadruplicate , & c . , increasing the denomination still by unity in any number of proportionals . When ...
Seite 100
... proportionals . " [ The memory need not be burdened with these explanations until the propositione be studied to which they refer . ] XIII . This Permutando , or alternando , by permutation or alternately . phrase is used when there are ...
... proportionals . " [ The memory need not be burdened with these explanations until the propositione be studied to which they refer . ] XIII . This Permutando , or alternando , by permutation or alternately . phrase is used when there are ...
Seite 105
... proportionals , they are proportionals when taken inversely . Let A be to B , as C is to D. Inversely ( Def . 14 ) , B is to A as D is to C. G B E C H- D F Take of B and D any equimultiples whatever E and F ; and of A and Cany ...
... proportionals , they are proportionals when taken inversely . Let A be to B , as C is to D. Inversely ( Def . 14 ) , B is to A as D is to C. G B E C H- D F Take of B and D any equimultiples whatever E and F ; and of A and Cany ...
Seite 110
... proportionals , as one of the antecedents is to its consequent , so are all the antecedents taken together to all the consequents . G A B- L H E D M N- Let any number of magnitudes A , B , C , D , E , and F , be proportionals ; that is ...
... proportionals , as one of the antecedents is to its consequent , so are all the antecedents taken together to all the consequents . G A B- L H E D M N- Let any number of magnitudes A , B , C , D , E , and F , be proportionals ; that is ...
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The Elements of Geometry: Or, the First Six Books, with the Eleventh and ... Euclides Keine Leseprobe verfügbar - 2016 |
Häufige Begriffe und Wortgruppen
A B and CD ABC is equal adjacent angles altitude angle ABC angle ACB angle BAC angle EDF 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 AB 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
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Seite 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.
Seite 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.
Seite 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.
Seite 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...
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 19 - THEOREM. IF two triangles have two sides of the one equal to two sides of the...