The Elements of EuclidJohnson and Warner, 1811 - 518 Seiten |
Im Buch
Ergebnisse 1-5 von 70
Seite 11
... diameter of a circle is a straight line drawn through the cen- tre , and terminated both ways by the circumference . XVIII . A semicircle is the figure contained by a diameter and the part of the circumference cut off by that diameter ...
... diameter of a circle is a straight line drawn through the cen- tre , and terminated both ways by the circumference . XVIII . A semicircle is the figure contained by a diameter and the part of the circumference cut off by that diameter ...
Seite 39
... diameter is the straight line joining two of its opposite angles . Let ACDB be a parallelogram , of which BC is a diameter ; the opposite sides and angles of the figure are equal to one another ; and the diameter BC bisects it . Because ...
... diameter is the straight line joining two of its opposite angles . Let ACDB be a parallelogram , of which BC is a diameter ; the opposite sides and angles of the figure are equal to one another ; and the diameter BC bisects it . Because ...
Seite 40
... diameter BC divides the paral- lelogram ACDB into two equal parts . Q. E. D. , € 4. 1 . See Note . See the 2d and 3d fi . gures . a 54. 1 . PROP . XXXV . THEOR . PARALLELOGRAMS upon the same base , and between the same parallels , are ...
... diameter BC divides the paral- lelogram ACDB into two equal parts . Q. E. D. , € 4. 1 . See Note . See the 2d and 3d fi . gures . a 54. 1 . PROP . XXXV . THEOR . PARALLELOGRAMS upon the same base , and between the same parallels , are ...
Seite 41
... EBCA is equal to DBCF , because b 35. 1 . they are upon the same base BC , and between the same parallels BC , EF ; and the triangle ABC is the half of the parallelo- F Book I. gram EBCA , because the diameter AB bisects OF EUCLID . 41.
... EBCA is equal to DBCF , because b 35. 1 . they are upon the same base BC , and between the same parallels BC , EF ; and the triangle ABC is the half of the parallelo- F Book I. gram EBCA , because the diameter AB bisects OF EUCLID . 41.
Seite 42
... diameter AB bisects it ; and the triangle DEF is the half of the parallelogram DEFH , be- cause the diameter DF bisects it : but the halves of equal 47. Ax . things are equal d ; therefore the triangle ABC is equal to the triangle DEF ...
... diameter AB bisects it ; and the triangle DEF is the half of the parallelogram DEFH , be- cause the diameter DF bisects it : but the halves of equal 47. Ax . things are equal d ; therefore the triangle ABC is equal to the triangle DEF ...
Andere Ausgaben - Alle anzeigen
Häufige Begriffe und Wortgruppen
altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore