The Elements of Euclid |
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Side 199
If there be two triangular prisms of the same altitude , the base of one of which is
a parallelogram , and the base of the other a triangle ; if the parallellogram be
double of the triangle , the prisms shall be equal to one another . Let the prisms ...
If there be two triangular prisms of the same altitude , the base of one of which is
a parallelogram , and the base of the other a triangle ; if the parallellogram be
double of the triangle , the prisms shall be equal to one another . Let the prisms ...
Side 205
of the triangle GFC : but when there are two prisms of the same altitude , of which
one has a parallelogram for its base ... to one another ; therefore the prism having
the parallelogram EBFG for its base , and the straight line KH opposite to it , is ...
of the triangle GFC : but when there are two prisms of the same altitude , of which
one has a parallelogram for its base ... to one another ; therefore the prism having
the parallelogram EBFG for its base , and the straight line KH opposite to it , is ...
Side 207
parts in the points N , Y by the same planes : therefore the prisms LXCOMN ,
RVFSTY are of the same altitude ; and therefore as the base LXC to the base
RVF ; that is , as the triangle ABC to the triangle DEF , so ( Cor . 32 . 11 . ) is the
prism ...
parts in the points N , Y by the same planes : therefore the prisms LXCOMN ,
RVFSTY are of the same altitude ; and therefore as the base LXC to the base
RVF ; that is , as the triangle ABC to the triangle DEF , so ( Cor . 32 . 11 . ) is the
prism ...
Side 209
the solid Q is greater than the prisms in the pyramid DEFH . But it is also less ,
which is impossible . Therefore the base ABC is not to the base DEF , as the
pyramid ABCG to any solid which is less than the pyramid DEFH . In the same
manner ...
the solid Q is greater than the prisms in the pyramid DEFH . But it is also less ,
which is impossible . Therefore the base ABC is not to the base DEF , as the
pyramid ABCG to any solid which is less than the pyramid DEFH . In the same
manner ...
Side 211
From this it is manifest , that every pyramid is the third part of a prism which has
the same base , and is of an equal altitude with it ; for if the base of the prism be
any other figure than a triangle , it may be divided into prisms having triangular ...
From this it is manifest , that every pyramid is the third part of a prism which has
the same base , and is of an equal altitude with it ; for if the base of the prism be
any other figure than a triangle , it may be divided into prisms having triangular ...
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added altitude angle ABC angle BAC base BC is given centre circle circle ABCD circumference common cone contained cylinder definition demonstrated described diameter divided double draw drawn equal equal angles equiangular equimultiples Euclid excess fore four fourth given angle given in magnitude given in position given in species given magnitude given ratio given straight line gles greater Greek half join less likewise magnitude manner meet multiple Note opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition pyramid Q. E. D. PROP reason rectangle rectangle contained remaining right angles segment shown sides similar sine solid sphere square square of BC taken THEOR third triangle ABC wherefore whole
Populære avsnitt
Side 36 - If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.
Side 145 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Side 65 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Side 248 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.
Side 11 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Side 121 - 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 21 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Side 14 - To construct a triangle of which the sides shall be equal to three given straight lines ; but any two whatever of these lines must be greater than the third (20.
Side 80 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Side 133 - ... rectilineal figures are to one another in the duplicate ratio of their homologous sides.
Bibliografisk informasjon
| Tittel | The Elements of Euclid |
| Forfatter | Euclid |
| Redaktør | Robert Simson |
| Utgiver | Desilver, Thomas, 1838 |
| Original fra | Harvard University |
| Digitalisert | 29. sep 2005 |
| Lengde | 416 sider |
| Eksporter sitat | BiBTeX EndNote RefMan |