The first three books of Euclid's Elements of geometry, with theorems and problems, by T. TateLongman, Brown, Green, and Longmans, 1849 - 108 Seiten |
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Seite 6
... double of the same , are equal to one another . VII . Things which are halves of the same , are equal to one another . VIII . Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one ...
... double of the same , are equal to one another . VII . Things which are halves of the same , are equal to one another . VIII . Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one ...
Seite 29
... double ( 1. 34. ) of the triangle BDC ; and they are therefore equal to one another . B But , if the sides AD , EF , opposite to the base BC of the pa- rallelograms ABCD , EBCF , be not terminated in the same point ; then , because ABCD ...
... double ( 1. 34. ) of the triangle BDC ; and they are therefore equal to one another . B But , if the sides AD , EF , opposite to the base BC of the pa- rallelograms ABCD , EBCF , be not terminated in the same point ; then , because ABCD ...
Seite 32
... upon the same base , and between the same parallels ; the parallelogram shall be double of the triangle . Let the parallelogram ABCD and the triangle EBC be upon the same base BC , and between the same A 32 EUCLID'S ELEMENTS .
... upon the same base , and between the same parallels ; the parallelogram shall be double of the triangle . Let the parallelogram ABCD and the triangle EBC be upon the same base BC , and between the same A 32 EUCLID'S ELEMENTS .
Seite 33
... double of the triangle EBC . B D E C But the parallelogram Join AC ; then the triangle ABC is equal ( 1. 37. ) to the triangle EBC , because they are upon the same base BC , and between the same parallels BC , AE . ABCD is double ( 1 ...
... double of the triangle EBC . B D E C But the parallelogram Join AC ; then the triangle ABC is equal ( 1. 37. ) to the triangle EBC , because they are upon the same base BC , and between the same parallels BC , AE . ABCD is double ( 1 ...
Seite 37
... double ( 1. 41. ) of the triangle ABD , because they are upon the same base BD , and between the same parallels , BD , AL ; and the square GB is double of the triangle FBC , because these also are upon the same base FB , and between the ...
... double ( 1. 41. ) of the triangle ABD , because they are upon the same base BD , and between the same parallels , BD , AL ; and the square GB is double of the triangle FBC , because these also are upon the same base FB , and between the ...
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The First Three Books of Euclid's Elements of Geometry from the Text of Dr ... Euclid,Thomas Tate Keine Leseprobe verfügbar - 2014 |
The First Three Books of Euclid's Elements of Geometry from the Text of Dr ... Euclid,Thomas Tate Keine Leseprobe verfügbar - 2014 |
Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 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...
Seite 5 - Let it be granted that a straight line may be drawn from any one point to any other point.
Seite 20 - If two triangles have two sides of the one equal to two sides of the...
Seite 30 - Parallelograms upon equal bases, and between the same parallels, are equal to one another.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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.