The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh and Twelfth ; the Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored ; Also the Book of Euclid's Data, in Like Manner CorrectedDesilver, 1829 - 516 sider |
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Side 119
... excess of the first above the second , is to the second , as the excess of the third above the fourth , is to the fourth . 17th Prop . book 5 . XVII . Convertendo , by conversion ; when there are four proportionals , and it is inferred ...
... excess of the first above the second , is to the second , as the excess of the third above the fourth , is to the fourth . 17th Prop . book 5 . XVII . Convertendo , by conversion ; when there are four proportionals , and it is inferred ...
Side 120
... excess above the fourth . Prop . E , book 5 . XVIII . Ex æquali ( sc . distantia ) , or ex æquo , from equality of distance when there is any number of magnitudes more than two , and as many others , so that they are proportionals when ...
... excess above the fourth . Prop . E , book 5 . XVIII . Ex æquali ( sc . distantia ) , or ex æquo , from equality of distance when there is any number of magnitudes more than two , and as many others , so that they are proportionals when ...
Side 142
... excess above the second , as the third to its excess above the fourth . Let AB be to BE , as CD to DF ; then BA is to A AE , as DC to CF. Because AB is to BE , as CD to DF , by divi- sion ( 17. 5. ) , AE is to EB , as CF to FD , and by ...
... excess above the second , as the third to its excess above the fourth . Let AB be to BE , as CD to DF ; then BA is to A AE , as DC to CF. Because AB is to BE , as CD to DF , by divi- sion ( 17. 5. ) , AE is to EB , as CF to FD , and by ...
Side 148
... excess of the first and fifth shall be to the second , as the excess of the third and sixth to the fourth . The demon- stration of this is the same with that of the proposition , if divi- sion be used instead of composition . COR . 2 ...
... excess of the first and fifth shall be to the second , as the excess of the third and sixth to the fourth . The demon- stration of this is the same with that of the proposition , if divi- sion be used instead of composition . COR . 2 ...
Side 184
... excess of EF above C , and similar and similarly situated to D ; but D is similar to EF , therefore ( 21. 6. ) also KM is similar to EF ; let KL * See Note . be the homologous side to EG , and LM , 184 BOOK VI . THE ELEMENTS OF EUCLID .
... excess of EF above C , and similar and similarly situated to D ; but D is similar to EF , therefore ( 21. 6. ) also KM is similar to EF ; let KL * See Note . be the homologous side to EG , and LM , 184 BOOK VI . THE ELEMENTS OF EUCLID .
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2018 |
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altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference co-sine cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
Populære avsnitt
Side 9 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 81 - The angles in the same segment of a circle are equal to one another.
Side 315 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Side 33 - 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 49 - 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 96 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Side 155 - 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 22 - ANY two angles of a triangle are together less than two right angles.
Side 25 - Let A, B, C be the three given straight lines, of which any two whatever are greater than the third, viz.
Side 24 - Any two sides of a triangle are together greater than the third side.