The first three books of Euclid's Elements of geometry, with theorems and problems, by T. Tate |
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Side 7
But it has been shown that BC is equal to BG ; wherefore Al and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line A L is equal to BC . Wherefore from the given ...
But it has been shown that BC is equal to BG ; wherefore Al and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line A L is equal to BC . Wherefore from the given ...
Side 22
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 A c is greater than A B. Wherefore the angle , & c . Q. E. D. PROP . XX .
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 A c is greater than A B. Wherefore the angle , & c . Q. E. D. PROP . XX .
Side 23
... DB ; but it has been shown that BA , A C are greater than B E , EC ; much more then are BA , A C greater than BD , А D B DC . Again , because the exterior angle of a triangle is greater than the interior and opposite angle ( 1.
... DB ; but it has been shown that BA , A C are greater than B E , EC ; much more then are BA , A C greater than BD , А D B DC . Again , because the exterior angle of a triangle is greater than the interior and opposite angle ( 1.
Side 27
than the base E F ; but it is not ; therefore 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 .
than the base E F ; but it is not ; therefore 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 .
Side 33
to the angle GKD ; and it was shown that the angle AGK is equal to the angle GhF ; therefore also A GK is equal to GKV ; and they are alternate angles ; therefore AB is parallel ( I. 27. ) to CD . Wherefore straight lines , & c .
to the angle GKD ; and it was shown that the angle AGK is equal to the angle GhF ; therefore also A GK is equal to GKV ; and they are alternate angles ; therefore AB is parallel ( I. 27. ) to CD . Wherefore straight lines , & c .
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The first three books of Euclid's Elements of geometry, with theorems and ... Euclid,Thomas Tate Uten tilgangsbegrensning - 1849 |
The First Three Books of Euclid's Elements of Geometry from the Text of Dr ... Euclid,Thomas Tate Ingen forhåndsvisning tilgjengelig - 2014 |
The First Three Books of Euclid's Elements of Geometry from the Text of Dr ... Euclid,Thomas Tate Ingen forhåndsvisning tilgjengelig - 2014 |
Vanlige uttrykk og setninger
A B C ABCD adjacent angle ABC angle ACB angle BAC angle equal base BC BC is equal bisect centre circle ABC circumference coincide common construct demonstrated describe diameter divided double draw equal angles equal to FB equilateral exterior angle extremity figure fore four given point given straight line greater impossible interior join less Let ABC likewise lines AC manner meet opposite angles opposite sides parallel parallelogram pass perpendicular PROB produced Q. E. D. PROP rectangle A B rectangle contained remaining remaining angle right angles segment semicircle shown sides squares of AC straight line A B Take taken THEOR third touch touches the circle triangle ABC twice the rectangle Wherefore whole