The first three books of Euclid's Elements of geometry, with theorems and problems, by T. TateLongman, Brown, Green, and Longmans, 1849 - 108 sider |
Inni boken
Resultat 1-5 av 16
Side 16
... angle DEB , and CEB to EAD . Because the straight line AE makes C with CD the angles CEA , AED , these angles are ... exterior angle is greater than either of the interior opposite angles . Let ABC be a triangle , and let its side ...
... angle DEB , and CEB to EAD . Because the straight line AE makes C with CD the angles CEA , AED , these angles are ... exterior angle is greater than either of the interior opposite angles . Let ABC be a triangle , and let its side ...
Side 17
... angles together are less than two right angles . A C D Produce BC to D ; and because ACD is the exterior angle of the triangle B ABC , ACD is greater ( 1. 16. ) than the interior and opposite angle ABC ; to each of these add the angle ...
... angles together are less than two right angles . A C D Produce BC to D ; and because ACD is the exterior angle of the triangle B ABC , ACD is greater ( 1. 16. ) than the interior and opposite angle ABC ; to each of these add the angle ...
Side 19
... angle . Let the two straight lines BD , CD be drawn from B , C , the ends of the side BC of the triangle ABC , to ... exterior angle of a triangle is greater than the interior and opposite angle ( 1. 16. ) , the exterior angle BDC ...
... angle . Let the two straight lines BD , CD be drawn from B , C , the ends of the side BC of the triangle ABC , to ... exterior angle of a triangle is greater than the interior and opposite angle ( 1. 16. ) , the exterior angle BDC ...
Side 23
... angle GCB is equal to the angle DFE ; but DFE is , by the hypothesis , equal to the angle BCA ; wherefore aso the ... exterior angle BHA of the triangle AHC is equal to its interior and opposite angle BCA , which is impossible ( 1 ...
... angle GCB is equal to the angle DFE ; but DFE is , by the hypothesis , equal to the angle BCA ; wherefore aso the ... exterior angle BHA of the triangle AHC is equal to its interior and opposite angle BCA , which is impossible ( 1 ...
Side 24
... exterior angle AEF is greater ( 1. 16. ) than the interior and opposite angle EFG ; but it is also equal A E toit ( Hyp . ) , which is impossible : therefore A B and CD being pro- C duced do not meet towards B , D. In like manner it ...
... exterior angle AEF is greater ( 1. 16. ) than the interior and opposite angle EFG ; but it is also equal A E toit ( Hyp . ) , which is impossible : therefore A B and CD being pro- C duced do not meet towards B , D. In like manner it ...
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 alternate angles angle ABC angle ACB angle AGH angle BAC angle BCD angle EDF angle equal angles CAB 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 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.