The school edition. Euclid's Elements of geometry, the first six books, by R. Potts. corrected and enlarged. corrected and improved [including portions of book 11,12].1864 |
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Side 32
... similar reason , EF is equal to BC ; wherefore AD is equal to EF ; ( ax . 1. ) and DE is common ; therefore the whole , or the remainder AE , is equal to the whole , or the remainder DF ; ( ax . 2 or 3. ) and AB is equal to DC ; ( 1. 24 ...
... similar reason , EF is equal to BC ; wherefore AD is equal to EF ; ( ax . 1. ) and DE is common ; therefore the whole , or the remainder AE , is equal to the whole , or the remainder DF ; ( ax . 2 or 3. ) and AB is equal to DC ; ( 1. 24 ...
Side 44
... similar distinction of triangles . Def . XXX - XXXIV . The definitions of quadrilateral figures are liable to objection . All of them , except the trapezium , fall under the general idea of a parallelogram ; but as Euclid defined ...
... similar distinction of triangles . Def . XXX - XXXIV . The definitions of quadrilateral figures are liable to objection . All of them , except the trapezium , fall under the general idea of a parallelogram ; but as Euclid defined ...
Side 49
... similar way may be supplied the reserved premiss in every enthy- meme . The conclusion of two enthymemes may form the major and minor premiss of a third syllogism , and so on , and thus any process of reasoning is reduced to the ...
... similar way may be supplied the reserved premiss in every enthy- meme . The conclusion of two enthymemes may form the major and minor premiss of a third syllogism , and so on , and thus any process of reasoning is reduced to the ...
Side 51
... similar construction the less of two given straight lines may be produced , so that the less together with the part produced may be equal to the greater . Prop . III . This problem admits of two solutions , and it is left unde- termined ...
... similar construction the less of two given straight lines may be produced , so that the less together with the part produced may be equal to the greater . Prop . III . This problem admits of two solutions , and it is left unde- termined ...
Side 55
... similar way , it may be shewn that BC cannot be otherwise than equal to EF . If ACB , DFE be both right angles : the case falls under Euc . 1. 26 . Prop . XXVII . Alternate angles are defined to be the two angles which two straight ...
... similar way , it may be shewn that BC cannot be otherwise than equal to EF . If ACB , DFE be both right angles : the case falls under Euc . 1. 26 . Prop . XXVII . Alternate angles are defined to be the two angles which two straight ...
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Vanlige uttrykk og setninger
A₁ ABCD AC is equal Algebraically angle ABC angle ACB angle BAC angle equal Apply Euc base BC chord circle ABC constr describe a circle diagonals diameter divided double draw equal angles equiangular equilateral triangle equimultiples Euclid Euclid's Elements exterior angle Geometrical given angle given circle given line given point given straight line gnomon greater hypotenuse inscribed intersection isosceles triangle less Let ABC line BC lines be drawn multiple opposite angles parallelogram parallelopiped pentagon perpendicular polygon problem produced Prop proportionals proved Q.E.D. PROPOSITION radius ratio rectangle contained rectilineal figure remaining angle right angles right-angled triangle segment semicircle shew shewn similar solid angle square on AC tangent THEOREM touch the circle trapezium triangle ABC twice the rectangle vertex vertical angle wherefore
Populære avsnitt
Side 112 - Guido, with a burnt stick in his hand, demonstrating on the smooth paving-stones of the path, that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides.
Side 83 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square...
Side 48 - If two triangles have two sides of the one equal to two sides of the other, each to each ; and...
Side 238 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth; if the 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 198 - A LESS magnitude is said to be a part of a greater magnitude, when the less measures the greater, that is, ' when the less is contained a certain number of times exactly in the greater.
Side 271 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.
Side 81 - 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 115 - angle in a segment' is the angle contained by two straight lines drawn from any point in the circumference of the segment, to the extremities of the straight line which is the base of the segment.
Side 341 - On the same base, and on the same side of it, there cannot be two triangles...
Side 24 - ... twice as many right angles as the figure has sides ; therefore all the angles of the figure together with four right angles, are equal to twice as many right angles as the figure has sides.