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 54
... rectangle contained by the whole line thus pro- duced , and the part of it produced , together with the square of half the line bisected , is equal to the square of the straight line which is made up of the half and the part produced ...
... rectangle contained by the whole line thus pro- duced , and the part of it produced , together with the square of half the line bisected , is equal to the square of the straight line which is made up of the half and the part produced ...
Side 55
... rectangle AB , BC is double of AK , for BK is equal ( Cor . 4. 2. ) to BC therefore the gnomon AKF , to- gether with the square CK , is equal to twice the rectangle AB , BC : to each of D these equals add HF , which is equal to the ...
... rectangle AB , BC is double of AK , for BK is equal ( Cor . 4. 2. ) to BC therefore the gnomon AKF , to- gether with the square CK , is equal to twice the rectangle AB , BC : to each of D these equals add HF , which is equal to the ...
Side 56
... rectangle CK is equal ( 36. 1. ) to BN , and GR to RN ; but CK is equal ( 43. 1. ) to RN , because they are the complements of the parallelogram CO ; therefore also BN is equal to GR ; and the four rectangles BN , CK , GR , RN are ...
... rectangle CK is equal ( 36. 1. ) to BN , and GR to RN ; but CK is equal ( 43. 1. ) to RN , because they are the complements of the parallelogram CO ; therefore also BN is equal to GR ; and the four rectangles BN , CK , GR , RN are ...
Side 60
... rectangle AB , BH is equal to the square of AH . A F G H B Produce GH to K ; because the straight line AC is bisected in E , and produced to the point F , the rectangle CF , FA , toge- ther with the square of AE , is equal ( 6. 2. ) to ...
... rectangle AB , BH is equal to the square of AH . A F G H B Produce GH to K ; because the straight line AC is bisected in E , and produced to the point F , the rectangle CF , FA , toge- ther with the square of AE , is equal ( 6. 2. ) to ...
Side 61
... rectangle BC , CD . A Because the straight line BD is divided into two parts in the point C , the square of BD is equal ( 4. 2. ) to the squares of BC , CD , and twice the rectangle BC , CD : to each of these equals add the square of DA ...
... rectangle BC , CD . A Because the straight line BD is divided into two parts in the point C , the square of BD is equal ( 4. 2. ) to the squares of BC , CD , and twice the rectangle BC , CD : to each of these equals add the square of DA ...
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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 |
Vanlige uttrykk og setninger
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.