The Elements of Euclid, the parts read in the University of Cambridge [book 1-6 and parts of book 11,12] with geometrical problems, by J.W. Colenso1846 |
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Side 9
... less ( 1. 3 ) , and join FC , GB . Then , because AF is equal to AG , and AB to AC ( Hyp . ) , the two sides FA , AC are equal to the two GA , AB , each to each , and they contain the angle FAG common to the two triangles AFC , AGB ...
... less ( 1. 3 ) , and join FC , GB . Then , because AF is equal to AG , and AB to AC ( Hyp . ) , the two sides FA , AC are equal to the two GA , AB , each to each , and they contain the angle FAG common to the two triangles AFC , AGB ...
Side 11
... less , and join DC : Then , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both triangles , the two sides DB , BC are equal to the two AC , CB , each to each , and the angle DBC is equal to the angle ACB ( Hyp ...
... less , and join DC : Then , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both triangles , the two sides DB , BC are equal to the two AC , CB , each to each , and the angle DBC is equal to the angle ACB ( Hyp ...
Side 15
... less to the greater -- which is absurd : Where- B E fore two straight lines cannot have a common segment . PROP . XII . PROB . To draw a straight line , perpendicular to a given straight line of unlimited length , from a given point ...
... less to the greater -- which is absurd : Where- B E fore two straight lines cannot have a common segment . PROP . XII . PROB . To draw a straight line , perpendicular to a given straight line of unlimited length , from a given point ...
Side 18
... less to the greater -- which is absurd Therefore BE is not in the same straight line with BC : And in like manner it may be demon- strated , that no other can be in the same straight line with it but BD : Therefore BD is in the same ...
... less to the greater -- which is absurd Therefore BE is not in the same straight line with BC : And in like manner it may be demon- strated , that no other can be in the same straight line with it but BD : Therefore BD is in the same ...
Side 20
... less than two right angles . Let ABC be a triangle : any two of its angles are together less than two right angles . Produce BC to D : Then , because ACD is the ex- terior angle of the triangle ABC , ACD is greater than the interior and ...
... less than two right angles . Let ABC be a triangle : any two of its angles are together less than two right angles . Produce BC to D : Then , because ACD is the ex- terior angle of the triangle ABC , ACD is greater than the interior and ...
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The Elements of Euclid, the Parts Read in the University of Cambridge [Book ... Euclides Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
ABCD adjacent angles angle ABC angle ACB angle BAC angle BCD angle EDF angle equal base BC BC is equal centre chord circle ABC circumference cuts the circle diameter double draw equal angles equal to F equiangular equilateral triangle equimultiples exterior angle fore given circle given line given point given straight line gnomon greater ratio inscribed intersection isosceles triangle less Let ABC Let the straight lines be drawn lines drawn meet multiple opposite angles opposite sides parallel to BC parallelogram pentagon perpendicular plane polygon PROB produced proportionals Q.E.D. PROP rectangle contained rectilineal figure remaining angle right angles right-angled triangle segment semicircle shew shewn square of AC straight line &c straight line AB THEOR touches the circle triangle ABC twice the rectangle Wherefore
Populære avsnitt
Side 42 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Side 4 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 33 - F, which is the common vertex of the triangles: that is », together with four right angles. 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.
Side 62 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Side 22 - If from the ends of a side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle.
Side 58 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Side 146 - ... may be demonstrated from what has been said of the pentagon : and likewise a circle may be inscribed in a given equilateral and equiangular hexagon, and circumscribed about it, by a method like to that used for the pentagon.
Side 194 - 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 2 - A circle is a plane figure contained by one line, which is called the circumference, and is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another : 16.
Side 69 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.