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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Resultater 1-5 af 45
Side 3
... segment of a circle is the figure contained by a straight line , and the part of the circumference it cuts off . ] This definition is repeated in Book III . Definition VI . XX . Rectilineal [ or , rectilinear , that is , formed of ...
... segment of a circle is the figure contained by a straight line , and the part of the circumference it cuts off . ] This definition is repeated in Book III . Definition VI . XX . Rectilineal [ or , rectilinear , that is , formed of ...
Side 13
... segment ; that is , they cannot coincide in part without coinciding altogether . If it be possible , let the two straight lines ABC , ABD , have the segment AB common to both of them . From the point B draw ( I. 11 ) BE at right angles ...
... segment ; that is , they cannot coincide in part without coinciding altogether . If it be possible , let the two straight lines ABC , ABD , have the segment AB common to both of them . From the point B draw ( I. 11 ) BE at right angles ...
Side 14
... segment . Q.E. D. E B D In Playfair's edition of the Elements , this corollary is drawn from the defective definition of a straight line , which he has substituted for Euclid's . Exercises . - 1 . From the extremity of a given straight ...
... segment . Q.E. D. E B D In Playfair's edition of the Elements , this corollary is drawn from the defective definition of a straight line , which he has substituted for Euclid's . Exercises . - 1 . From the extremity of a given straight ...
Side 32
... drawn from the opposite angles of a parallelogram to any point in a diagonal , divide it into equal triangles on opposite sides of the segments of the diagonal PROP . XXXIX . THEOREM . Equal triangles upon the 32 EUCLID'S ELEMENTS .
... drawn from the opposite angles of a parallelogram to any point in a diagonal , divide it into equal triangles on opposite sides of the segments of the diagonal PROP . XXXIX . THEOREM . Equal triangles upon the 32 EUCLID'S ELEMENTS .
Side 39
... segments of that side is equal to the difference of the squares of the other two sides . DEFINITION . - In any right - angled triangle , the side opposite to the right angle is called the hypothenuse , and the other sides , or legs ...
... segments of that side is equal to the difference of the squares of the other two sides . DEFINITION . - In any right - angled triangle , the side opposite to the right angle is called the hypothenuse , and the other sides , or legs ...
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The Elements of Geometry: Or, the First Six Books, with the Eleventh and ... Euclides Ingen forhåndsvisning - 2016 |
Almindelige termer og sætninger
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
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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...