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 153
... compounded of the ratio which the first has to the second , and of the ratio which the second has to the third , and of the ratio which the third has to the fourth , and so on unto the last magnitude . For example , if A , B , C , H 3 ...
... compounded of the ratio which the first has to the second , and of the ratio which the second has to the third , and of the ratio which the third has to the fourth , and so on unto the last magnitude . For example , if A , B , C , H 3 ...
Side 154
... compounded of the ratio of A to B , and of the ratio of B to C , and of the ratio of C to D ; or , the ratio of A to D is said to be compounded of the ratios of A to B , B to C , and C to D. And if A has to B the same ratio which E has ...
... compounded of the ratio of A to B , and of the ratio of B to C , and of the ratio of C to D ; or , the ratio of A to D is said to be compounded of the ratios of A to B , B to C , and C to D. And if A has to B the same ratio which E has ...
Side 190
... and F to GB , and CH and E to HD ; therefore AB and F together are greater than ( I. ax . 4. ) Therefore , if four magnitudes , & c . and E. Q. E. D. PROP . F. - THEOREM . Ratios which are compounded 190 THE ELEMENTS OF EUCLID .
... and F to GB , and CH and E to HD ; therefore AB and F together are greater than ( I. ax . 4. ) Therefore , if four magnitudes , & c . and E. Q. E. D. PROP . F. - THEOREM . Ratios which are compounded 190 THE ELEMENTS OF EUCLID .
Side 191
... compounded of the ratios of A to B , and B to C , is the same with the ratio of D to F , which is compounded of the ratios of D to E , and E to F. And in like manner the proposition may be demonstrated , whatever be the number of ratios ...
... compounded of the ratios of A to B , and B to C , is the same with the ratio of D to F , which is compounded of the ratios of D to E , and E to F. And in like manner the proposition may be demonstrated , whatever be the number of ratios ...
Side 192
... compounded of the ratios of N to O , and O to P , which are the same with the ratios of E to F , and G to H. And it ... compounded of several ratios be the same to a ratio which is compounded of several other ratios ; and if one of the ...
... compounded of the ratios of N to O , and O to P , which are the same with the ratios of E to F , and G to H. And it ... compounded of several ratios be the same to a ratio which is compounded of several other ratios ; and if one of 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...