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 8
... base BC shall be equal to the base EF , and the triangle ABC to the triangle DEF , and the other angles shall be equal , each to each , to which the equal sides are opposite , viz . the angle ABC to the angle DEF , and the angle ACB to ...
... base BC shall be equal to the base EF , and the triangle ABC to the triangle DEF , and the other angles shall be equal , each to each , to which the equal sides are opposite , viz . the angle ABC to the angle DEF , and the angle ACB to ...
Side 9
... base EF ; because , B coinciding with E , and C with F , if BC does not coincide with EF , two straight lines would enclose a space - which is impossible ( Ax . 10 ) ; therefore the base BC shall coincide with the base EF , and be equal ...
... base EF ; because , B coinciding with E , and C with F , if BC does not coincide with EF , two straight lines would enclose a space - which is impossible ( Ax . 10 ) ; therefore the base BC shall coincide with the base EF , and be equal ...
Side 10
... base of the triangle ABC : And it has been proved that the angle FBC is equal to the angle GCB , which are the angles upon the other side of the base . Wherefore , The angles at the base & c . Q. E.D. COROLLARY . Hence every equilateral ...
... base of the triangle ABC : And it has been proved that the angle FBC is equal to the angle GCB , which are the angles upon the other side of the base . Wherefore , The angles at the base & c . Q. E.D. COROLLARY . Hence every equilateral ...
Side 11
... base DC is equal to the base AB ( 1. 4 ) , and the triangle DBC is equal to the triangle ACB , the less to the greater - which is absurd : Therefore AB is not unequal to AC , that is , it is equal to it . Wherefore , If two angles & c ...
... base DC is equal to the base AB ( 1. 4 ) , and the triangle DBC is equal to the triangle ACB , the less to the greater - which is absurd : Therefore AB is not unequal to AC , that is , it is equal to it . Wherefore , If two angles & c ...
Side 12
... base , & c . Q.E.D. PROP . VIII . 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 ...
... base , & c . Q.E.D. PROP . VIII . 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 ...
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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.