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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Página 6
... fore CA , AB , BC are equal to one another ; and the triangle ABC is therefore equilateral , and it is described upon the given straight line AB . Q. E. F PROP . II . PROB . From a given point to draw a straight line equal to a given ...
... fore CA , AB , BC are equal to one another ; and the triangle ABC is therefore equilateral , and it is described upon the given straight line AB . Q. E. F PROP . II . PROB . From a given point to draw a straight line equal to a given ...
Página 9
... , AGB - there . fore ( 1.4 ) the base FC is equal to the base D ' GB , and the triangle AFC to the triangle F B A C G E AGB , and the remaining angles of the one to the remaining angles of the other , each to each , BOOK I. 9.
... , AGB - there . fore ( 1.4 ) the base FC is equal to the base D ' GB , and the triangle AFC to the triangle F B A C G E AGB , and the remaining angles of the one to the remaining angles of the other , each to each , BOOK I. 9.
Página 15
... fore , from the given point C , in the given straight line AB , CF has been drawn at right angles to AB . Q. E. F. COR . By the help of this problem , it may be demon- strated that two straight lines cannot have a common segment . If it ...
... fore , from the given point C , in the given straight line AB , CF has been drawn at right angles to AB . Q. E. F. COR . By the help of this problem , it may be demon- strated that two straight lines cannot have a common segment . If it ...
Página 27
... AH : Then because BH is equal to EF , and AB to DE ( Hyp . ) , the two AB , BH are equal to the two DE , EF , each to each , and they contain equal angles ( Hyp . ) — there- fore the base AH is equal to the base DF BOOK I. 27.
... AH : Then because BH is equal to EF , and AB to DE ( Hyp . ) , the two AB , BH are equal to the two DE , EF , each to each , and they contain equal angles ( Hyp . ) — there- fore the base AH is equal to the base DF BOOK I. 27.
Página 28
Euclides John William Colenso (bp. of Natal). fore the base AH is equal to the base DF , and the triangle ABH to the triangle DEF , and the other angles to the other angles , each to each , to which the equal sides are opposite ...
Euclides John William Colenso (bp. of Natal). fore the base AH is equal to the base DF , and the triangle ABH to the triangle DEF , and the other angles to the other angles , each to each , to which the equal sides are opposite ...
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The Elements of Euclid, the Parts Read in the University of Cambridge [Book ... Euclides Sin vista previa disponible - 2016 |
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 4 - Let it be granted that a straight line may be drawn from any one point to any other point.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.