The first three books of Euclid's Elements of geometry, with theorems and problems, by T. TateLongman, Brown, Green, and Longmans, 1849 - 108 pages |
From inside the book
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Page 3
... diameter and the part of the circumference cut off by the diameter . XIX . " A segment of a circle is the figure contained by a straight line , and the circumference it cuts off . ” XX . Rectilineal figures are those which are contained ...
... diameter and the part of the circumference cut off by the diameter . XIX . " A segment of a circle is the figure contained by a straight line , and the circumference it cuts off . ” XX . Rectilineal figures are those which are contained ...
Page 28
... diameter is the straight line joining two of its opposite angles . Let ACDB be a parallelogram , of which BC is a diameter ; the opposite sides and angles of the figure are equal to one another ; and the diameter BC bisects it . A B ...
... diameter is the straight line joining two of its opposite angles . Let ACDB be a parallelogram , of which BC is a diameter ; the opposite sides and angles of the figure are equal to one another ; and the diameter BC bisects it . A B ...
Page 29
... diameter bisects them ; for AB being equal to CD , and BC common , the two AB , BC are equal to the two DC , CB , each to each ; and the angle ABC is equal to the angle BCD ; therefore the triangle ABC is equal ( 1. 4. ) to the triangle ...
... diameter bisects them ; for AB being equal to CD , and BC common , the two AB , BC are equal to the two DC , CB , each to each ; and the angle ABC is equal to the angle BCD ; therefore the triangle ABC is equal ( 1. 4. ) to the triangle ...
Page 31
... diameter AB bisects it ( 1 . 34. ) ; and the triangle DBC is the half of the parallelogram DBCF , because the diameter DC bisects it : But the halves of equal things are equal ( Ax . 7. ) ; therefore the triangle ABC is equal to the ...
... diameter AB bisects it ( 1 . 34. ) ; and the triangle DBC is the half of the parallelogram DBCF , because the diameter DC bisects it : But the halves of equal things are equal ( Ax . 7. ) ; therefore the triangle ABC is equal to the ...
Page 34
... diameter of any parallelogram , are equal to one another . E A H D K F Let ABCD be a parallelogram , of which the diameter is AC , and EH , FG the parallelograms about AC , that is , through which AC passes , and BK , KD the other ...
... diameter of any parallelogram , are equal to one another . E A H D K F Let ABCD be a parallelogram , of which the diameter is AC , and EH , FG the parallelograms about AC , that is , through which AC passes , and BK , KD the other ...
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.