The Elements of Euclid |
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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 ...
Side 177
the solid angle at K ; wherefore the plane AF coincides with the plane KP , and
the figure AF with the figure KP , because they are equal and similar to one
another : therefore the straight lines AE , EF , FB , coincide with KO , OP , PL ; and
the ...
the solid angle at K ; wherefore the plane AF coincides with the plane KP , and
the figure AF with the figure KP , because they are equal and similar to one
another : therefore the straight lines AE , EF , FB , coincide with KO , OP , PL ; and
the ...
Side 179
what multiple soever the base LF is of the base AF , the same multiple is the solid
LV of the solid AV : for the same reason , whatever multiple the base NF is of the
base HF , the same multiple is the solid NV of the solid ED ; and if the base LF ...
what multiple soever the base LF is of the base AF , the same multiple is the solid
LV of the solid AV : for the same reason , whatever multiple the base NF is of the
base HF , the same multiple is the solid NV of the solid ED ; and if the base LF ...
Side 184
lelopiped ; but the solid CM , of which the base is ACBL , to which FDHM is the
opposite parallelogram , is equal ( 29 . 11 . ) to the solid CP , of which the base is
the parallelogram ACBL , to which ORQP NK мн A C is the one opposite ...
lelopiped ; but the solid CM , of which the base is ACBL , to which FDHM is the
opposite parallelogram , is equal ( 29 . 11 . ) to the solid CP , of which the base is
the parallelogram ACBL , to which ORQP NK мн A C is the one opposite ...
Side 185
the solid AE to the solid LR : for the same reason , because the solid
parallelopiped CR is cut by the plane LMFD , which is parallel to the opposite
planes CP , BR ; as the base CD to the base LQ , so P F R is the solid CF to the
NTME solid LR ...
the solid AE to the solid LR : for the same reason , because the solid
parallelopiped CR is cut by the plane LMFD , which is parallel to the opposite
planes CP , BR ; as the base CD to the base LQ , so P F R is the solid CF to the
NTME solid LR ...
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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 |