The first three books of Euclid's Elements of geometry, with theorems and problems, by T. Tate1851 - 139 sider |
Inni boken
Side 46
... square upon a given straight line . Let AB be the given straight line ; it is required to describe a square upon AB . From the point A draw ( I. 11. ) AC at right angles to AB ; and make ( 1. 3. ) A D equal to AB , and through the point ...
... square upon a given straight line . Let AB be the given straight line ; it is required to describe a square upon AB . From the point A draw ( I. 11. ) AC at right angles to AB ; and make ( 1. 3. ) A D equal to AB , and through the point ...
Side 47
... squares described upon BA , AC . On BC describe ( 1.46 . ) the square BDEC , and on BA , AC the squares GB , HC ; and through a draw ( 1. 31. ) AL parallel to BD or CE , and join AD , FC ; then , because each of the angles BAC , BAG is ...
... squares described upon BA , AC . On BC describe ( 1.46 . ) the square BDEC , and on BA , AC the squares GB , HC ; and through a draw ( 1. 31. ) AL parallel to BD or CE , and join AD , FC ; then , because each of the angles BAC , BAG is ...
Side 48
... squares GB , HC upon BA , AC : Wherefore the square upon the side BC is equal to the squares upon the sides BA , AC . Therefore , in any right angled triangle , & c . Q.E. D. PROP . XLVIII . THEOR . If the square described upon one of ...
... squares GB , HC upon BA , AC : Wherefore the square upon the side BC is equal to the squares upon the sides BA , AC . Therefore , in any right angled triangle , & c . Q.E. D. PROP . XLVIII . THEOR . If the square described upon one of ...
Side 49
... AC , the angle BAC is a right angle . D From the point A draw ( 1. 11. ) AD at right angles to AC , and make AD ... squares of DA , AC , are equal to the squares of BA , AC : But the square of DC is equal ( 1.47 . ) to B C the squares of ...
... AC , the angle BAC is a right angle . D From the point A draw ( 1. 11. ) AD at right angles to AC , and make AD ... squares of DA , AC , are equal to the squares of BA , AC : But the square of DC is equal ( 1.47 . ) to B C the squares of ...
Side 51
... square of the whole line . Let the straight line AB be divided into any two parts in the point c ; the rectangle contained by A B , BC , together with the rectangle * A A B , AC , shall be equal to the square of A B. Upon AB describe ...
... square of the whole line . Let the straight line AB be divided into any two parts in the point c ; the rectangle contained by A B , BC , together with the rectangle * A A B , AC , shall be equal to the square of A B. Upon AB describe ...
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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 angles angle ABC angle ACB angle BAC angle equal angles BGH base BC BC is equal bisect centre circle ABC circumference diameter divided double draw a straight equal angles equal circles equal straight lines equal to FB exterior angle given point given rectilineal angle given straight line gnomon greater half a right hypotenuse interior and opposite isosceles triangle less Let ABC Let the straight line be drawn opposite angles parallel parallelogram perpendicular PROB produced Q. E. D. PROP rectangle AE rectangle contained rectilineal figure remaining angle right angles segment semicircle side BC square of AC straight line AB straight line AC straight line drawn THEOR touches the circle trapezium triangle ABC twice the rectangle vertex vertical angle