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 7
... wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC . Wherefore from the given point a a straight line AL has been drawn equal ...
... wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC . Wherefore from the given point a a straight line AL has been drawn equal ...
Seite 8
... wherefore also the point c shall coincide with the point F , be- cause the straight line AC is equal to DF ( Hyp . ) . But the point B coincides with the point E ; wherefore the base BC shall coin- cide with the base EF , because the ...
... wherefore also the point c shall coincide with the point F , be- cause the straight line AC is equal to DF ( Hyp . ) . But the point B coincides with the point E ; wherefore the base BC shall coin- cide with the base EF , because the ...
Seite 9
... wherefore the triangles are equal ( 1. 4. ) , and their remaining angles , each to each , to which the equal sides are opposite ; therefore the angle FBC is equal to the angle GCB , and the angle BCF to the angle CBG : And , since it ...
... wherefore the triangles are equal ( 1. 4. ) , and their remaining angles , each to each , to which the equal sides are opposite ; therefore the angle FBC is equal to the angle GCB , and the angle BCF to the angle CBG : And , since it ...
Seite 10
... Wherefore , if two angles , & c . Q. E. D. B COR . Hence every equiangular triangle is also equilateral . PROP . VII . THEOR . Upon the same base , and on the same side of it , there can- not be two triangles that have their sides which ...
... Wherefore , if two angles , & c . Q. E. D. B COR . Hence every equiangular triangle is also equilateral . PROP . VII . THEOR . Upon the same base , and on the same side of it , there can- not be two triangles that have their sides which ...
Seite 11
... wherefore the angle FDC is likewise A greater than BCD ; much more then is the angle BDC greater than the angle BCD . Again , because CB is equal to DB , the angle BDC is equal ( 1. 5. ) to the angle BCD ; but BDC has been proved to be ...
... wherefore the angle FDC is likewise A greater than BCD ; much more then is the angle BDC greater than the angle BCD . Again , because CB is equal to DB , the angle BDC is equal ( 1. 5. ) to the angle BCD ; but BDC has been proved to be ...
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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.