The first three books of Euclid's Elements of geometry, with theorems and problems, by T. TateLongman, Brown, Green, and Longmans, 1849 - 108 sider |
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Side 17
... angle BCG , that is ( I. 15. ) , the angle ACD , is greater than the angle ABC . Therefore , if one side , & c ... ACB ; therefore the angles ACD , ACB are greater than the angles ABC , ACB ; but ACD , ACB are together equal ( 1 . 13 ...
... angle BCG , that is ( I. 15. ) , the angle ACD , is greater than the angle ABC . Therefore , if one side , & c ... ACB ; therefore the angles ACD , ACB are greater than the angles ABC , ACB ; but ACD , ACB are together equal ( 1 . 13 ...
Side 18
... angle ABC is greater than the angle BCA ; the side AC is likewise greater than the side AB . A For , if it be not ... ACB ; but it is not ; therefore AC is not equal to AB ; neither is it less ; because then the angle ABC would be less ...
... angle ABC is greater than the angle BCA ; the side AC is likewise greater than the side AB . A For , if it be not ... ACB ; but it is not ; therefore AC is not equal to AB ; neither is it less ; because then the angle ABC would be less ...
Side 27
... angle ACD is equal to the two interior and opposite angles CAB , ABC ; to these equals add the angle ACB , and the angles ACD , ACB are equal to the three angles CBA , BAC , ACB ; but the angles ACD , ACB are equal ( 1. 13. ) to two right ...
... angle ACD is equal to the two interior and opposite angles CAB , ABC ; to these equals add the angle ACB , and the angles ACD , ACB are equal to the three angles CBA , BAC , ACB ; but the angles ACD , ACB are equal ( 1. 13. ) to two right ...
Side 28
... triangle ABC to the tri- angle BCD , and the other angles to the other angles ( 1.4 . ) , each to each , to which the equal sides are opposite ; therefore the angle ACB is equal to the angle CBD ; and because the straight line BC meets ...
... triangle ABC to the tri- angle BCD , and the other angles to the other angles ( 1.4 . ) , each to each , to which the equal sides are opposite ; therefore the angle ACB is equal to the angle CBD ; and because the straight line BC meets ...
Side 29
... angle of the one to the third angle of the other ( 1. 26. ) , viz . the side AB to the side CD , and AC to BD , and ... ACB , the whole angle ABD is equal to the whole angle ACD : And the angle BAC has been shown to be equal to the angle ...
... angle of the one to the third angle of the other ( 1. 26. ) , viz . the side AB to the side CD , and AC to BD , and ... ACB , the whole angle ABD is equal to the whole angle ACD : And the angle BAC has been shown to be equal to the angle ...
Andre utgaver - Vis alle
The first three books of Euclid's Elements of geometry, with theorems and ... Euclides Uten tilgangsbegrensning - 1851 |
The First Three Books of Euclid's Elements of Geometry from the Text of Dr ... Euclid,Thomas Tate Ingen forhåndsvisning tilgjengelig - 2014 |
The First Three Books of Euclid's Elements of Geometry from the Text of Dr ... Euclid,Thomas Tate Ingen forhåndsvisning tilgjengelig - 2014 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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...
Side 5 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 20 - If two triangles have two sides of the one equal to two sides of the...
Side 30 - Parallelograms upon equal bases, and between the same parallels, are equal to one another.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.