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 17
... angle BCG , that is ( I. 15. ) , the angle ACD , is greater than the angle ABC . Therefore , if one side , & c ... CAB , ABC , are less than two right angles . Therefore any two angles , & c . Q. E. D. PROP . XVIII . THEOR . The greater side ...
... angle BCG , that is ( I. 15. ) , the angle ACD , is greater than the angle ABC . Therefore , if one side , & c ... CAB , ABC , are less than two right angles . Therefore any two angles , & c . Q. E. D. PROP . XVIII . THEOR . The greater side ...
Seite 26
... angle AGH is equal ( 1. 29. ) A. to the angle GHF . Again , because the straight line GHK cuts the parallel E ... CAB , ABC , and the three interior angles of the triangles , viz . ABC , BCA , CAB , are together equal to two right angles ...
... angle AGH is equal ( 1. 29. ) A. to the angle GHF . Again , because the straight line GHK cuts the parallel E ... CAB , ABC , and the three interior angles of the triangles , viz . ABC , BCA , CAB , are together equal to two right angles ...
Seite 27
... angle ECD is equal to the in- terior and opposite angle ABC ; but the angle ACE was shown to be equal to the angle BAC ; therefore the whole exterior angle ACD is equal to the two interior and opposite angles CAB , ABC ; to these equals add ...
... angle ECD is equal to the in- terior and opposite angle ABC ; but the angle ACE was shown to be equal to the angle BAC ; therefore the whole exterior angle ACD is equal to the two interior and opposite angles CAB , ABC ; to these equals add ...
Seite 71
... CAB , viz . the angles CA B , ABC , BCA , are equal to two right angles : But the angle CAB is equal ( III . 21. ) to the angle CDB , be- cause they are in the same segment BADC , and the angle ACB is equal to the angle ADB , because ...
... CAB , viz . the angles CA B , ABC , BCA , are equal to two right angles : But the angle CAB is equal ( III . 21. ) to the angle CDB , be- cause they are in the same segment BADC , and the angle ACB is equal to the angle ADB , because ...
Seite 77
... angle in a semicircle is a right angle ; but the angle in a segment greater than a semicircle is less than a right ... CAB , but the circumference of the less segment ADC falls within the right angle CAF . " And this is all that is meant ...
... angle in a semicircle is a right angle ; but the angle in a segment greater than a semicircle is less than a right ... CAB , but the circumference of the less segment ADC falls within the right angle CAF . " And this is all that is meant ...
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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.