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 8
... base BC shall coin- cide with the base EF , because the point B coinciding with E , and c with F , if the base BC does not coincide with the base EF , two straight lines would inclose a space , which is impossible ( Ax . 10. ) . Therefore ...
... base BC shall coin- cide with the base EF , because the point B coinciding with E , and c with F , if the base BC does not coincide with the base EF , two straight lines would inclose a space , which is impossible ( Ax . 10. ) . Therefore ...
Page 9
... base of an Isosceles triangle are equal to one another ; and , if the equal ... BC is common to the two angles BFC , CGB ; wherefore the triangles are equal ... base of the triangle ABC : And it has also been proved that the angle FBC is ...
... base of an Isosceles triangle are equal to one another ; and , if the equal ... BC is common to the two angles BFC , CGB ; wherefore the triangles are equal ... base of the triangle ABC : And it has also been proved that the angle FBC is ...
Page 10
... base , & c . Q. E. D. COROLLARY . Hence every equilateral triangle is also equi- angular . PROP . VI . THEOR . If ... BC common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; and the angle DBC is equal to ...
... base , & c . Q. E. D. COROLLARY . Hence every equilateral triangle is also equi- angular . PROP . VI . THEOR . If ... BC common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; and the angle DBC is equal to ...
Page 11
... base CD are equal ( 1. 5. ) to one another , but the angle ECD is greater than the angle BCD ; wherefore the angle ... BC equal to the base EF . The angle BAC is equal to the angle EDF . For if the triangle ABC be applied D G CE F to DEF ...
... base CD are equal ( 1. 5. ) to one another , but the angle ECD is greater than the angle BCD ; wherefore the angle ... BC equal to the base EF . The angle BAC is equal to the angle EDF . For if the triangle ABC be applied D G CE F to DEF ...
Page 12
... base BC coincides with the base EF ; the sides BA , AC cannot but coincide with the sides ED , DF ; wherefore likewise the angle BAC coincides with the angle EDF , and is equal ( Ax . 8. ) to it . Therefore if two triangles , & c ...
... base BC coincides with the base EF ; the sides BA , AC cannot but coincide with the sides ED , DF ; wherefore likewise the angle BAC coincides with the angle EDF , and is equal ( Ax . 8. ) to it . Therefore if two triangles , & c ...
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.