The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 páginas |
Dentro del libro
Resultados 1-5 de 32
Página 6
... demonstrated . PROPOSITION V. - THEOREM . 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 also be equal . LET abc be an ...
... demonstrated . PROPOSITION V. - THEOREM . 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 also be equal . LET abc be an ...
Página 7
... demonstrated , that the whole angle abg is equal to the whole a cf , the parts of which , the angles c bg , bcf are also equal ; the remaining angle abc is therefore equal to the remaining angle a cb , which are the angles at the base ...
... demonstrated , that the whole angle abg is equal to the whole a cf , the parts of which , the angles c bg , bcf are also equal ; the remaining angle abc is therefore equal to the remaining angle a cb , which are the angles at the base ...
Página 8
... demonstrated to be greater than it ; which is vertices , as d , be within the other triangle acb ; e , f ; therefore , because ac is equal to ad in the triangle acd , the angles ecd , fdc upon the other side of the base cd are equal ( i ...
... demonstrated to be greater than it ; which is vertices , as d , be within the other triangle acb ; e , f ; therefore , because ac is equal to ad in the triangle acd , the angles ecd , fdc upon the other side of the base cd are equal ( i ...
Página 10
... demonstrated , that two straight lines cannot have a common segment . If it be possible , let the two straight lines abc , abd have the seg- ment ab common to both of them . From the point b draw be at right angles to ab ; and because ...
... demonstrated , that two straight lines cannot have a common segment . If it be possible , let the two straight lines abc , abd have the seg- ment ab common to both of them . From the point b draw be at right angles to ab ; and because ...
Página 12
... demonstrated to be equal to the same three angles ; and things that are equal to the same are equal ( 1 ax . ) to one another ; therefore the angles cbe , ebd are equal to the angles dba , abc ; but cbe , ebd are two right angles ...
... demonstrated to be equal to the same three angles ; and things that are equal to the same are equal ( 1 ax . ) to one another ; therefore the angles cbe , ebd are equal to the angles dba , abc ; but cbe , ebd are two right angles ...
Otras ediciones - Ver todas
Términos y frases comunes
a b c abcd adjacent angles angle a cb angle abc angle bac angle edf angle equal base bc bc is equal bisected centre circle abc describe diameter double draw equal angles equal straight lines equal to f equimultiples ex æquali exterior angle fore four magnitudes fourth given circle given straight line gnomon greater ratio greater than f ILLUSTRATED LONDON inscribe less LET abc LET the straight likewise multiple opposite angle parallel parallelogram pentagon perpendicular Q. E. D. PROPOSITION rectangle a d rectangle contained remaining angle right angles segment shewn square of a c square of eg straight line a b straight line ab straight line bc tiple touches the circle triangle abc triangle def twice the rectangle
Pasajes populares
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 : XVI.
Página 42 - 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.
Página 4 - Let it be granted that a straight line may be drawn from any one point to any other point.
Página 21 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Página 29 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Página 38 - 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 of...
Página 15 - If, from the ends of the 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. Let...
Página 13 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Página 4 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Página 126 - 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.