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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Seite 9
... THEOR . The angles at the base of an isosceles triangle are equal to one another ; and , if the equal sides be produced , the angles upon the other side of the base shall be equal . Let ABC be an isosceles triangle , of which the side ...
... THEOR . The angles at the base of an isosceles triangle are equal to one another ; and , if the equal sides be produced , the angles upon the other side of the base shall be equal . Let ABC be an isosceles triangle , of which the side ...
Seite 12
... THEOR . If two triangles have two sides of the one equal to two sides of the other , each to each , and have also their bases equal , the angle which is contained by the two sides of the one shall be equal to the angle contained by the ...
... THEOR . If two triangles have two sides of the one equal to two sides of the other , each to each , and have also their bases equal , the angle which is contained by the two sides of the one shall be equal to the angle contained by the ...
Seite 17
... THEOR . If , at a point in a straight line , two other straight lines , upon the opposite sides of it , make the adjacent angles together equal to two right angles , these two straight lines shall be in one and the same straight line ...
... THEOR . If , at a point in a straight line , two other straight lines , upon the opposite sides of it , make the adjacent angles together equal to two right angles , these two straight lines shall be in one and the same straight line ...
Seite 18
... THEOR . If two straight lines cut one another , the vertical , or op- posite , angles shall be equal . Let the two straight lines AB , CD cut one another in the point E : the angle AEC shall be equal to the angle BED , and the angle AED ...
... THEOR . If two straight lines cut one another , the vertical , or op- posite , angles shall be equal . Let the two straight lines AB , CD cut one another in the point E : the angle AEC shall be equal to the angle BED , and the angle AED ...
Seite 19
... THEOR . If one side of a triangle be produced , the exterior angle is greater than either of the interior opposite angles . Let ABC be a triangle , and let its side BC be pro- duced to D : the exterior angle ACD is greater than either ...
... THEOR . If one side of a triangle be produced , the exterior angle is greater than either of the interior opposite angles . Let ABC be a triangle , and let its side BC be pro- duced to D : the exterior angle ACD is greater than either ...
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The Elements of Euclid, the Parts Read in the University of Cambridge [Book ... Euclides Keine Leseprobe verfügbar - 2016 |
Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 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.
Seite 4 - Let it be granted that a straight line may be drawn from any one point to any other point.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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.