The Elements of Euclid |
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Side 184
Solid parallelopipeds which are upon equal bases and of the same altitude , are
equal to one another . * Let the solid parallelopipeds AE , CF be upon equal
bases AB , CD , and be of the same altitude ; the solid AE is equal to the solid CF
.
Solid parallelopipeds which are upon equal bases and of the same altitude , are
equal to one another . * Let the solid parallelopipeds AE , CF be upon equal
bases AB , CD , and be of the same altitude ; the solid AE is equal to the solid CF
.
Side 185
But let the solid parallelopipeds SE , CF be upon equal bases SB , CD , and be of
the same altitude , and let their insisting straight lines be at right angles to the
bases ; and place the bases SB , CD in the same plane , so that CL , LB be in a ...
But let the solid parallelopipeds SE , CF be upon equal bases SB , CD , and be of
the same altitude , and let their insisting straight lines be at right angles to the
bases ; and place the bases SB , CD in the same plane , so that CL , LB be in a ...
Side 190
Make then CT equal to AG , and complete the solid parallelopiped CV of which
the base is NP , and the altitude CT . H olan Because the solid AB is equal to the
solid CD , therefore the А CN solid AB is to the solid CV , as ( 7 . 5 . ) the solid CD
...
Make then CT equal to AG , and complete the solid parallelopiped CV of which
the base is NP , and the altitude CT . H olan Because the solid AB is equal to the
solid CD , therefore the А CN solid AB is to the solid CV , as ( 7 . 5 . ) the solid CD
...
Side 191
is the solid AB to the solid CV ; for the solids AB , CV are of the same altitude ;
and as MC to CT , so is the base MP to the base PT , and the solid GD to the solid
( 25 . 11 . ) CV : and therefore as the solid AB to the solid CV , so is the solid CD
to ...
is the solid AB to the solid CV ; for the solids AB , CV are of the same altitude ;
and as MC to CT , so is the base MP to the base PT , and the solid GD to the solid
( 25 . 11 . ) CV : and therefore as the solid AB to the solid CV , so is the solid CD
to ...
Side 195
to one another : therefore the solids KO , DH are of the same altitude ; and they
are upon equal bases LM , EF , and therefore they are equal ( 31 . 11 . ) to one
another : but the solid KO is described from the three straight lines A , B , C , and
the ...
to one another : therefore the solids KO , DH are of the same altitude ; and they
are upon equal bases LM , EF , and therefore they are equal ( 31 . 11 . ) to one
another : but the solid KO is described from the three straight lines A , B , C , and
the ...
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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 |