The Elements of Euclid |
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Side 164
But the plane passing through ED , GH is the plane BH ; therefore AF is
perpendicular to the plane BH ; therefore , from the given point A , above the
plane BA , the straight line AF is drawn perpendicular to that plane . Which was to
be done .
But the plane passing through ED , GH is the plane BH ; therefore AF is
perpendicular to the plane BH ; therefore , from the given point A , above the
plane BA , the straight line AF is drawn perpendicular to that plane . Which was to
be done .
Side 166
plane with it ) the angles GBA , BGH are together equal ( 29 . ... to the plane
through AB , BC : and it is perpendicular to the plane through DE , EF : therefore
BG is perpendicular to each of the planes through AB , BC , and DE , EF : but
planes ...
plane with it ) the angles GBA , BGH are together equal ( 29 . ... to the plane
through AB , BC : and it is perpendicular to the plane through DE , EF : therefore
BG is perpendicular to each of the planes through AB , BC , and DE , EF : but
planes ...
Side 167
KL , MN are cut by the plane EBDX , the common sections EX , BD , are parallel (
16 . 11 . ) . For the same reason , because the two parallel planes GH , KL are cut
by H the plane AXFC , the common G / A sections AC , XF , are parallel : and ...
KL , MN are cut by the plane EBDX , the common sections EX , BD , are parallel (
16 . 11 . ) . For the same reason , because the two parallel planes GH , KL are cut
by H the plane AXFC , the common G / A sections AC , XF , are parallel : and ...
Side 168
If two planes cutting one another be each of them perpendicular to a third plane ;
their common section shall be perpendicular to the same plane . Let the two
planes AB , BC be each of them perpendicular to a third plane , and let BD be the
...
If two planes cutting one another be each of them perpendicular to a third plane ;
their common section shall be perpendicular to the same plane . Let the two
planes AB , BC be each of them perpendicular to a third plane , and let BD be the
...
Side 169
EVERY solid angle is contained by plane angles which together are less than
four right angles . First , let the solid angle at A be contained by three plane
angles BAC , CAD , DAB . These three together are less than four right angles ,
Take in ...
EVERY solid angle is contained by plane angles which together are less than
four right angles . First , let the solid angle at A be contained by three plane
angles BAC , CAD , DAB . These three together are less than four right angles ,
Take in ...
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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 |