The College Euclid: Comprising the First Six and the Parts of the Eleventh and Twelfth Books Read at the Universities ... By A. K. Isbister1865 |
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Side 152
... multiple of a less , when the greater is measured by the less ; that is , when the greater contains the less a ... multiple of the first be less than that of the second , the multiple of the third is also less than that of the fourth ...
... multiple of a less , when the greater is measured by the less ; that is , when the greater contains the less a ... 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 153
... multiple of the first be greater than that of the second , the multiple of the third is also greater than that of the fourth . VI . Magnitudes which have the same ratio are called proportionals . When four magnitudes are proportionals ...
... multiple of the first be greater than that of the second , the multiple of the third is also greater than that of the fourth . VI . Magnitudes which have the same ratio are called proportionals . When four magnitudes are proportionals ...
Side 156
... multiple of a greater magnitude is greater than the same multiple of a less . IV . That magnitude , of which a multiple is greater than the same mul- tiple of another , is greater than that other magnitude . PROP . I. - THEOREM . If any ...
... multiple of a greater magnitude is greater than the same multiple of a less . IV . That magnitude , of which a multiple is greater than the same mul- tiple of another , is greater than that other magnitude . PROP . I. - THEOREM . If any ...
Side 157
... multiple AB is of E , the same multiple is AB and CD together , of E and F together . Therefore , if any magnitudes , how many soever , be equimultiples of as many , each of each ; whatsoever multiple any one of them is of its part ...
... multiple AB is of E , the same multiple is AB and CD together , of E and F together . Therefore , if any magnitudes , how many soever , be equimultiples of as many , each of each ; whatsoever multiple any one of them is of its part ...
Side 158
... multiple , & c . Q. E. D. Cor . From this it is plain , that if any number of magnitudes AB , BG , GH be multiples ... multiple of C , that the whole of the last , viz . DL , is of F. A B G H D E K L T C F PROP . III - THEOREM . If the ...
... multiple , & c . Q. E. D. Cor . From this it is plain , that if any number of magnitudes AB , BG , GH be multiples ... multiple of C , that the whole of the last , viz . DL , is of F. A B G H D E K L T C F PROP . III - THEOREM . If the ...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ... Euclides Uten tilgangsbegrensning - 1865 |
The College Euclid: Comprising the First Six and the Parts of the Eleventh ... Euclides Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
ABCD AC is equal adjacent angles angle ABC angle ACB angle BAC angle equal base BC bisect Book centre circle ABC circumference compounded constr DEMONSTRATION diameter double draw Edition English equal angles equal straight lines equal to BC equiangular equilateral and equiangular equimultiples Euclid exterior angle four magnitudes fourth French given circle given point given rectilineal angle given straight line gnomon Grammar greater ratio inscribed isosceles triangle join less Let ABC multiple opposite angles parallel parallelogram pentagon perpendicular plane polygon proportionals proposition Q. E. D. PROP rectangle contained rectilineal figure References-Prop remaining angle right angles segment similar solid angle square of AC straight line AC THEOREM third three straight lines touches the circle triangle ABC twice the rectangle wherefore
Populære avsnitt
Side 140 - 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. either the sides adjacent to the equal...
Side xiv - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Side 310 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.
Side 33 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Side vi - If a straight line be divided into any two parts, four times the rectangle contained ~by the whole line and one of the parts, together with the square on the other part, is equal to the square on the straight line which is made up of the whole and that part.
Side 310 - 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 xxxvii - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Side 69 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square of the other part.
Side 287 - If any point be taken in the diameter of a circle which is not the centre, of all the straight lines which can be drawn from it to the circumference, the greatest is that in which the centre is, and the other part of that diameter is the least...