The Elements of Euclid |
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Side 216
cone , which together shall be less than the excess of the cone above the third
part of the cylinder . Let these be the segments upon AE , EB , BF , FC , CG , GD ,
DH , HA . Therefore the rest of the cone , that is , the pyramid , of which the base
is ...
cone , which together shall be less than the excess of the cone above the third
part of the cylinder . Let these be the segments upon AE , EB , BF , FC , CG , GD ,
DH , HA . Therefore the rest of the cone , that is , the pyramid , of which the base
is ...
Side 274
But if B and C together be less than A ; then , because it is required that B , C , D
together be greater than A , from each of these taking away B , C , the remaining
one D must be greater than the excess of A above B and C ; take therefore any ...
But if B and C together be less than A ; then , because it is required that B , C , D
together be greater than A , from each of these taking away B , C , the remaining
one D must be greater than the excess of A above B and C ; take therefore any ...
Side 301
If the excess of a magnitude , above a given magnitude , has a given ratio to
another magnitude ; the excess of both together above a given magnitude shall
have to that other a given ratio : and if the excess of two magnitudes together
above a ...
If the excess of a magnitude , above a given magnitude , has a given ratio to
another magnitude ; the excess of both together above a given magnitude shall
have to that other a given ratio : and if the excess of two magnitudes together
above a ...
Side 306
than AG : - and AB , AG are given ; therefore the remainder BG is given : and
because C F D as AE to CF , so is AG to CD , and so - is ( 19 . 5 . ) EG to FD ; the
ratio of EG to FE is given : and GB is given ; therefore EG , the excess of EB
above a ...
than AG : - and AB , AG are given ; therefore the remainder BG is given : and
because C F D as AE to CF , so is AG to CD , and so - is ( 19 . 5 . ) EG to FD ; the
ratio of EG to FE is given : and GB is given ; therefore EG , the excess of EB
above a ...
Side 307
ratio to the second , the same excess shall have a given ratio to the first ; as is
evident from thd 9th dat . PROP . XXV . 17 . If there be three magnitudes , the
excess of the first whereof above a given magnitude has a given ratio to the
second ...
ratio to the second , the same excess shall have a given ratio to the first ; as is
evident from thd 9th dat . PROP . XXV . 17 . If there be three magnitudes , the
excess of the first whereof above a given magnitude has a given ratio to the
second ...
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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 |