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 38
... whole , or the remainder AE , is equal ( 2. or 3. Ax . ) to the whole , or the remainder DF ; AB also is equal to DC ; and the two FA E D F A D E B C B C ; EA , AB are therefore equal to the two FD , DC , each to each and the exterior ...
... whole , or the remainder AE , is equal ( 2. or 3. Ax . ) to the whole , or the remainder DF ; AB also is equal to DC ; and the two FA E D F A D E B C B C ; EA , AB are therefore equal to the two FD , DC , each to each and the exterior ...
Side 43
... whole triangle ABC is equal to the whole ADC ; therefore the remaining com- plement BK is equal to the remaining complement KD . Where- fore the complements , & c . Q. E. D. PROP . XLIV . PROB . To a given straight line to apply a ...
... whole triangle ABC is equal to the whole ADC ; therefore the remaining com- plement BK is equal to the remaining complement KD . Where- fore the complements , & c . Q. E. D. PROP . XLIV . PROB . To a given straight line to apply a ...
Side 45
... whole rectilineal figure ABCD is equal to the whole parallelogram KFLM ; therefore the parallelogram KFLM has been described equal to the given rectilineal figure ABCD , having the angle FKM equal to the given angle E. Which was to be ...
... whole rectilineal figure ABCD is equal to the whole parallelogram KFLM ; therefore the parallelogram KFLM has been described equal to the given rectilineal figure ABCD , having the angle FKM equal to the given angle E. Which was to be ...
Side 47
... whole angle DBA is equal ( 2. Ax . ) to the whole FBC and because the two sides AB , BD are equal to the two FB , BC , each to each , and the angle DBA equal to the angle FBC ; therefore the base AD is equal ( 4. 1. ) to the base FC ...
... whole angle DBA is equal ( 2. Ax . ) to the whole FBC and because the two sides AB , BD are equal to the two FB , BC , each to each , and the angle DBA equal to the angle FBC ; therefore the base AD is equal ( 4. 1. ) to the base FC ...
Side 50
... whole and each of the parts , are together equal to the square of the whole line . Let the straight line AB be divided into A any two parts in the point C ; the rectangle contained by AB , BC , together with the rectangle AB , AC ...
... whole and each of the parts , are together equal to the square of the whole line . Let the straight line AB be divided into A any two parts in the point C ; the rectangle contained by AB , BC , together with the rectangle AB , AC ...
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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.