The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 páginas |
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Página 34
... twice the line joining the vertex and the middle of the base . 21. Each angle at the base of an isosceles triangle ... rectangle are equal to one another . 25. If any number of parallelograms be inscribed in a given parallelo- gram , the ...
... twice the line joining the vertex and the middle of the base . 21. Each angle at the base of an isosceles triangle ... rectangle are equal to one another . 25. If any number of parallelograms be inscribed in a given parallelo- gram , the ...
Página 37
... twice the rectangle contained by the parts . LET the straight line a b be divided into any two parts in c ; the ... rectangle contained by the unequal parts , together with the square of the line between the points of section , is equal ...
... twice the rectangle contained by the parts . LET the straight line a b be divided into any two parts in c ; the ... rectangle contained by the unequal parts , together with the square of the line between the points of section , is equal ...
Página 39
... twice the rectangle contained by the whole and that part , together with the square of the other part . LET the straight line ... rectangle a b , bc is double of a k , for bk is h equal ( ii . 4. cor . ) to bc : therefore the gnomon akf ...
... twice the rectangle contained by the whole and that part , together with the square of the other part . LET the straight line ... rectangle a b , bc is double of a k , for bk is h equal ( ii . 4. cor . ) to bc : therefore the gnomon akf ...
Página 43
... rectangle cf , fa , is equal to the square of ab ; and the figure fk is the rectangle contained by cf fa , for af is equal ... twice the rectangle bc , cd . Therefore , in obtuse - angled triangles , & c . Q. E. D. b c d PROPOSITION XIII ...
... rectangle cf , fa , is equal to the square of ab ; and the figure fk is the rectangle contained by cf fa , for af is equal ... twice the rectangle bc , cd . Therefore , in obtuse - angled triangles , & c . Q. E. D. b c d PROPOSITION XIII ...
Página 44
Euclides. PROPOSITION XIII . - THEOREM . In every triangle , the square of the side subtending any of the acute angles is less than the squares of the sides containing that angle , by twice the rectangle contained by either of these ...
Euclides. PROPOSITION XIII . - THEOREM . In every triangle , the square of the side subtending any of the acute angles is less than the squares of the sides containing that angle , by twice the rectangle contained by either of these ...
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Términos y frases comunes
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 perpendicular produced Q. E. D. PROPOSITION rectangle a d rectangle contained remaining angle right angles segment semicircle shewn square of a c straight line a b straight line ab straight line bc straight line drawn 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.