Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement of the Quadrature of the Circle and the Geometry of Solids |
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Resultat 1-5 av 47
Side 9
... are equalf ; therefore the remainder AL is equal f 19. Def . to the remainder : BG
: but it has been shown , that BC is g 3. Ax . equal to BG ; wherefore AL and BC
are each of them equal to BG ; therefore the straight line AL is equal to BCh . h 1.
... are equalf ; therefore the remainder AL is equal f 19. Def . to the remainder : BG
: but it has been shown , that BC is g 3. Ax . equal to BG ; wherefore AL and BC
are each of them equal to BG ; therefore the straight line AL is equal to BCh . h 1.
Side 22
... because then the ' angle ABC would be lessb than the angle ACB ; but it is not ;
therefore the side AC is not less than AB ; and it has been shown that it is not
equal to AB ; therefore AC is greater than AB . Wherefore the greater angle , & c .
... because then the ' angle ABC would be lessb than the angle ACB ; but it is not ;
therefore the side AC is not less than AB ; and it has been shown that it is not
equal to AB ; therefore AC is greater than AB . Wherefore the greater angle , & c .
Side 23
Again , because the two sides CE , ED , of the triangle CED , are greater than CD
, add DB to each of these ; therefore the sides CE , EB are greater than CD , DB ;
but it has been shown that BA , AC are greater than BE , EC ; much more then ...
Again , because the two sides CE , ED , of the triangle CED , are greater than CD
, add DB to each of these ; therefore the sides CE , EB are greater than CD , DB ;
but it has been shown that BA , AC are greater than BE , EC ; much more then ...
Side 27
1 . than the base EF ; E but it is not ; there B F fore the angle BAC is not less than
the angle EDF ; and it was shown that it is , not equal to it : therefore the angle
BAC is greater than the angle EDF . Wherefore , if two triangles , & c . Q. E. D. ...
1 . than the base EF ; E but it is not ; there B F fore the angle BAC is not less than
the angle EDF ; and it was shown that it is , not equal to it : therefore the angle
BAC is greater than the angle EDF . Wherefore , if two triangles , & c . Q. E. D. ...
Side 32
Again , because the straight line GK cuts the E parallel straight lines EF , H F CD ,
the angle GHF is equal a K к was shown that the angle C o AGK is equal to the
angle GHF ; therefore also AGK is equal to GKD ; and they are alternate angles ...
Again , because the straight line GK cuts the E parallel straight lines EF , H F CD ,
the angle GHF is equal a K к was shown that the angle C o AGK is equal to the
angle GHF ; therefore also AGK is equal to GKD ; and they are alternate angles ...
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Elements of Geometry: Containing the First Six Books of Euclid with a ... John Playfair Uten tilgangsbegrensning - 1855 |
Elements of Geometry: Containing the First Six Books of Euclid, with a ... Euclid,John Playfair Uten tilgangsbegrensning - 1853 |
Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Uten tilgangsbegrensning - 1847 |
Vanlige uttrykk og setninger
ABC is equal ABCD altitude angle ABC angle ACB angle BAC arch base bisected Book centre circle circle ABC circumference coincide common compounded contained cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular equilateral equimultiples exterior angle extremities fall figure fore fourth given straight line greater half inscribed interior join less Let ABC magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism PROB produced proportional proposition proved pyramid Q. E. D. PROP ratio reason rectangle contained rectilineal figure right angles segment shown sides similar solid space square taken THEOR third triangle ABC wherefore whole
Populære avsnitt
Side 121 - 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 42 - TO a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Side 63 - Therefore, in obtuse-angled triangles, &c. QED PROP. XIII. THEOREM. In every triangle, the square of the side subtending either of the acute angles is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle.
Side 3 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Side 183 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. Let AC, CF be equiangular parallelograms having the angle BCD equal to the angle ECG ; the ratio of the parallelogram AC to the parallelogram CF is the same with the ratio which is compounded •f the ratios of their sides.
Side 3 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Side 291 - 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 160 - ... extremities of the base shall have the same ratio which the other sides of the triangle have to one...
Side 10 - ... shall be greater than the base of the other. Let ABC, DEF be two triangles, which have the two sides AB, AC, equal to the two DE, DF, each to each, viz.
Side 14 - Therefore, upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extretnity equal to one another.
Bibliografisk informasjon
| Tittel | Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement of the Quadrature of the Circle and the Geometry of Solids |
| Forfatter | John Playfair |
| Utgiver | F. Nichols, 1806 |
| Original fra | University of Michigan |
| Digitalisert | 16. feb 2008 |
| ISBN | 0608378402, 9780608378404 |
| Lengde | 311 sider |
| Eksporter sitat | BiBTeX EndNote RefMan |