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 177
... straight lines , ABC , ABD , in the same plane , that have a common segment AB , which ( I. def . 3 , cor . ) is ... line EC is in it . For the same reason BC is in the same ; and ( hyp . ) EB is in it : therefore EC , CB , BE are in one ...
... straight lines , ABC , ABD , in the same plane , that have a common segment AB , which ( I. def . 3 , cor . ) is ... line EC is in it . For the same reason BC is in the same ; and ( hyp . ) EB is in it : therefore EC , CB , BE are in one ...
Page 2
... straight lines , whose positions in space are known , will be the single ... line A B ( pl . I. , fig . 1 ) , placed in any manner in space , we imagine ... straight line a b ; for they will be all included in the plane drawn through A B ...
... straight lines , whose positions in space are known , will be the single ... line A B ( pl . I. , fig . 1 ) , placed in any manner in space , we imagine ... straight line a b ; for they will be all included in the plane drawn through A B ...
Page 10
... AB BC is the excess of the length of the line AB above that of BC . AB means the square described straight line AB . Proposition 1. - Problem . upon the To describe an equilateral triangle on a given finite straight line . Let AB be the ...
... AB BC is the excess of the length of the line AB above that of BC . AB means the square described straight line AB . Proposition 1. - Problem . upon the To describe an equilateral triangle on a given finite straight line . Let AB be the ...
Page ix
... straight line A B .. · To test whether the visual planes of the two sights stand perpendicularly one upon the other . Surveyor's angle - mirror . Laws of the reflection of light by plane mirrors . Axis of incidence ; Angle of incidence ; ...
... straight line A B .. · To test whether the visual planes of the two sights stand perpendicularly one upon the other . Surveyor's angle - mirror . Laws of the reflection of light by plane mirrors . Axis of incidence ; Angle of incidence ; ...
Page 4
... line , and call it AB ; then we will rule a straight line CD across it . You see that you can place your ruler so that the straight line A will cut the curved one at two points , perhaps even more than two . Now take a straight line AB ...
... line , and call it AB ; then we will rule a straight line CD across it . You see that you can place your ruler so that the straight line A will cut the curved one at two points , perhaps even more than two . Now take a straight line AB ...
Other editions - View all
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.