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 σελίδες |
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Αποτελέσματα 1 - 5 από τα 100.
Σελίδα 4
... equal , and all its angles right angles . This definition is redundant . If the general definition annexed to the 34th Prop . of this book be considered , the square is only a species of parallelogram , viz . that which has one angle a ...
... equal , and all its angles right angles . This definition is redundant . If the general definition annexed to the 34th Prop . of this book be considered , the square is only a species of parallelogram , viz . that which has one angle a ...
Σελίδα 8
... angles contained by these sides equal to one another , their bases , or third sides , are equal ; the two triangles are equal ; and their other angles are equal , each to ... angle BAC is equal ( Hyp . ) to the angle 8 EUCLID'S ELEMENTS .
... angles contained by these sides equal to one another , their bases , or third sides , are equal ; the two triangles are equal ; and their other angles are equal , each to ... angle BAC is equal ( Hyp . ) to the angle 8 EUCLID'S ELEMENTS .
Σελίδα 9
... equal ( Ax . 8 ) to it . Wherefore , also , the whole triangle ABC coincides with the whole triangle DEF , and is , therefore , equal to it . And the remaining angles of the one coincide with the remaining angles of the other , and are ...
... equal ( Ax . 8 ) to it . Wherefore , also , the whole triangle ABC coincides with the whole triangle DEF , and is , therefore , equal to it . And the remaining angles of the one coincide with the remaining angles of the other , and are ...
Σελίδα 10
... equal to the angle CG B. Wherefore the two triangles BFC , CGB , are equal ( I. 4 ) , and their remaining angles are equal , each to each , viz . , those to which the equal sides are opposite . Therefore the angle FBC is equal to the ...
... equal to the angle CG B. Wherefore the two triangles BFC , CGB , are equal ( I. 4 ) , and their remaining angles are equal , each to each , viz . , those to which the equal sides are opposite . Therefore the angle FBC is equal to the ...
Σελίδα 11
... equal to one another , and likewise those terminated in the other extremity . If it be possible , upon the same base ... angles ECD , FDC upon the other side of the base CD are equal ( I. 5 ) to one another . But the angle ECD is greater ...
... equal to one another , and likewise those terminated in the other extremity . If it be possible , upon the same base ... angles ECD , FDC upon the other side of the base CD are equal ( I. 5 ) to one another . But the angle ECD is greater ...
Άλλες εκδόσεις - Προβολή όλων
The Elements of geometry; or, The first six books, with the eleventh and ... Euclides Πλήρης προβολή - 1855 |
The Elements of Geometry: Or, the First Six Books, with the Eleventh and ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 19 - THEOREM. IF two triangles have two sides of the one equal to two sides of the...