Euclid's Elements of geometry, books i. ii. iii. iv |
Inni boken
Resultat 1-5 av 5
Side 57
If a straight line be divided into any two parts , the squares on the whole line , and
on one of the parts , are equal to twice the rectangle contained by the whole and
that part , together with the squirre on the other part . H ( References Prop .
If a straight line be divided into any two parts , the squares on the whole line , and
on one of the parts , are equal to twice the rectangle contained by the whole and
that part , together with the squirre on the other part . H ( References Prop .
Side 58
CK and HF , is equal to twice the rectangle AB . BC , together with the square on
AC . 10 . But the gnomon AKF , together with the squares CK and HF , make up
the whole figure ADEB and CK , which are the squares on AB and BC . 11 .
CK and HF , is equal to twice the rectangle AB . BC , together with the square on
AC . 10 . But the gnomon AKF , together with the squares CK and HF , make up
the whole figure ADEB and CK , which are the squares on AB and BC . 11 .
Side 64
Therefore the remaining rectangle CF . ... But the figure FK is the rectangle
contained by CF and FA , for FA is equal to FG ; ( def . 30 . ) 10 . ... The square on
AB shall be greater than the squares on AC and CB , by twice the rectangle BC .
CD .
Therefore the remaining rectangle CF . ... But the figure FK is the rectangle
contained by CF and FA , for FA is equal to FG ; ( def . 30 . ) 10 . ... The square on
AB shall be greater than the squares on AC and CB , by twice the rectangle BC .
CD .
Side 65
Therefore the squares on BD and DA are equal to the squares on BC , CD , DA ,
and twice the rectangle BC . CD . 5 . But the square on BA is equal to the squares
on BD and DA , because the angle at D is a right angle ; ( I . 47 . ) 6 . And the ...
Therefore the squares on BD and DA are equal to the squares on BC , CD , DA ,
and twice the rectangle BC . CD . 5 . But the square on BA is equal to the squares
on BD and DA , because the angle at D is a right angle ; ( I . 47 . ) 6 . And the ...
Side 66
square on AC alone is less than the squares on CB and BA , by twice the
rectangle CB . BD . Case II . - Secondly , let AD fall without the triangle ABC .
Demonstration . - l . Because the angle at D is a right angle ( const . ) , the angle
ACB is ...
square on AC alone is less than the squares on CB and BA , by twice the
rectangle CB . BD . Case II . - Secondly , let AD fall without the triangle ABC .
Demonstration . - l . Because the angle at D is a right angle ( const . ) , the angle
ACB is ...
Hva folk mener - Skriv en omtale
Vi har ikke funnet noen omtaler på noen av de vanlige stedene.
Vanlige uttrykk og setninger
ABCD angle ABC angle BAC angle BCD angle equal assumed base base BC BC is equal bisected BOOK centre circle ABC circumference coincide common Conclusion Conclusion.—Therefore const Construction Construction.-1 Demonstration Demonstration.-1 describe diameter distance divided double draw drawn equilateral exterior angle extremities fall figure four given circle given point given rectilineal given straight line greater half Hypothesis.—Let inscribed join less manner meet opposite angle parallel parallelogram pass pentagon perpendicular produced Prop proved Q. E. D. PROPOSITION reason rectangle contained rectilineal figure References—Prop regular right angles segment semicircle shown sides Sought.-It is required square on AC Take third touches the circle triangle ABC twice the rectangle whole
Populære avsnitt
Side 25 - 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.
Side 2 - 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 99 - 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 4 - If a straight line meets two straight lines, so as to " make the two interior angles on the same side of it taken " together less than two right angles...
Side 66 - ... the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse...
Side 65 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Side 32 - F, which is the common vertex of the triangles ; that is, together with four right angles. Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Side 58 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced...
Side 88 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Side 33 - The straight lines which join the extremities of two equal and parallel straight lines towards the same parts, are also themselves equal and parallel.
Bibliografisk informasjon
| Tittel | Euclid's Elements of geometry, books i. ii. iii. iv Scot. sch. book assoc. Progressive series |
| Forfatter | Euclides |
| distribuert | 1862 |
| Original fra | Oxford University |
| Digitalisert | 19. apr 2006 |
| Eksporter sitat | BiBTeX EndNote RefMan |