The first three books of Euclid's Elements of geometry, with theorems and problems, by T. TateLongman, Brown, Green, and Longmans, 1849 - 108 pages |
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Page 36
... square upon a given straight line . Let AB be the given straight line ; it is required to describe a square upon A B. E From the point A draw ( 1. 11. ) AC at right angles to AB ; and make ( 1. 3. ) AD equal to AB , and through the ...
... square upon a given straight line . Let AB be the given straight line ; it is required to describe a square upon A B. E From the point A draw ( 1. 11. ) AC at right angles to AB ; and make ( 1. 3. ) AD equal to AB , and through the ...
Page 37
... square ( Def . 30. ) , and it is described upon the given straight line AB . Which was to be done . COR . Hence ... AC . G H On BC describe ( 1.46 . ) the square BDEC , and on BA , AC the squares GB , HC ; and through a draw ( 1. 31 ...
... square ( Def . 30. ) , and it is described upon the given straight line AB . Which was to be done . COR . Hence ... AC . G H On BC describe ( 1.46 . ) the square BDEC , and on BA , AC the squares GB , HC ; and through a draw ( 1. 31 ...
Page 38
... 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 ...
Page 40
... AC , shall be equal to the square of AB . D F E Upon AB describe ( 1. 46. ) the square ADEB , and through c draw ( 1. 31. ) CF parallel to AD or BE ; then AE is equal to the rectangles AF , CE ; and AE is the square of AB ; and AF is ...
... AC , shall be equal to the square of AB . D F E Upon AB describe ( 1. 46. ) the square ADEB , and through c draw ( 1. 31. ) CF parallel to AD or BE ; then AE is equal to the rectangles AF , CE ; and AE is the square of AB ; and AF is ...
Page 41
... square of the aforesaid part . Let the straight line AB be divided into two parts in the point c ; the rectangle AB , BC is equal to the rectangle AC , CB , together with the square of B C. B Upon BC describe ( 1. 46. ) the square CDEB , ...
... square of the aforesaid part . Let the straight line AB be divided into two parts in the point c ; the rectangle AB , BC is equal to the rectangle AC , CB , together with the square of B C. B Upon BC describe ( 1. 46. ) the square CDEB , ...
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The First Three Books of Euclid's Elements of Geometry from the Text of Dr ... Euclid,Thomas Tate No preview available - 2014 |
The First Three Books of Euclid's Elements of Geometry from the Text of Dr ... Euclid,Thomas Tate No preview available - 2014 |
Common terms and phrases
ABCD adjacent angles angle ABC angle ACB angle AGH angle BAC angle BCD angle CAB angle EDF angle equal angles CBA 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 fore given point given rectilineal angle given straight line gnomon greater half a right hypotenuse 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
Popular passages
Page 6 - 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...
Page 5 - Let it be granted that a straight line may be drawn from any one point to any other point.
Page 20 - If two triangles have two sides of the one equal to two sides of the...
Page 30 - Parallelograms upon equal bases, and between the same parallels, are equal to one another.
Page 17 - Any two angles of a triangle are together less than two right angles. Let ABC be any triangle ; any two of its angles together are less than two right angles.
Page 84 - IF from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it; if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, be equal to the square of the line which meets it, the line which meets it shall touch the circle.
Page 82 - If from any point without a circle two straight lines be drawn, one of -which cuts the circle, and the other touches it; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Page 11 - 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 extremity.
Page 19 - To make a triangle of which the sides shall be equal to three given straight lines, but any two whatever of these must be greater than the third, (i.
Page 7 - From the greater of two given straight lines to cut off a part equal to the less. Let AB and C be the two given straight lines, whereof AB is the greater.