The Elements of EuclidLongmans, Green and Company, 1866 - 376 páginas |
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Página 3
... diameter of a circle is a straight line drawn through the centre , and terminated both ways by the cir- cumference . xvII . A semicircle is the figure contained by a dia . meter and the part of the circumference it cuts off . XIX . A ...
... diameter of a circle is a straight line drawn through the centre , and terminated both ways by the cir- cumference . xvII . A semicircle is the figure contained by a dia . meter and the part of the circumference it cuts off . XIX . A ...
Página 34
... diameter bisects them , that is , divides them into two equal parts . N.B. - A parallelogram is a four - sided figure , of which the oppo- site sides are parallel ; and the diameter , or diagonal , is the straight line joining two of ...
... diameter bisects them , that is , divides them into two equal parts . N.B. - A parallelogram is a four - sided figure , of which the oppo- site sides are parallel ; and the diameter , or diagonal , is the straight line joining two of ...
Página 35
Euclides. 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 AB is parallel to CD , and BC meets them , the alternate ...
Euclides. 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 AB is parallel to CD , and BC meets them , the alternate ...
Página 37
... EBCA is equal B C to DBCF , because they are upon the same base BC , and between the same parallels BC , EF ( 1. 35 ) : But the triangle ABC is half of the parallelogram EBCA , E because the diameter AB bisects it ( 1. 34 ) BOOK I. 37.
... EBCA is equal B C to DBCF , because they are upon the same base BC , and between the same parallels BC , EF ( 1. 35 ) : But the triangle ABC is half of the parallelogram EBCA , E because the diameter AB bisects it ( 1. 34 ) BOOK I. 37.
Página 38
... diameter AB bisects it ( 1.34 ) ; and the triangle DEF is half of the parallelo- gram DEFH , because the diameter DF bisects it : the halves of equal things are equal ; therefore the triangle ABC is equal to the triangle DEF . Wherefore ...
... diameter AB bisects it ( 1.34 ) ; and the triangle DEF is half of the parallelo- gram DEFH , because the diameter DF bisects it : the halves of equal things are equal ; therefore the triangle ABC is equal to the triangle DEF . Wherefore ...
Términos y frases comunes
AB² ABCD AC² AD² adjacent angles angle ABC angle ACB angle BAC angle equal base BC BC is equal centre chord circle ABC circumference diameter double draw equal angles equal to F equiangular equilateral triangle equimultiples exterior angle fore given circle given line given point given rectilineal given straight line gnomon hypotenuse inscribed intersection isosceles triangle join less Let ABC lines be drawn lines drawn meet multiple opposite angles parallel to BC parallelogram perpendicular plane polygon PROB produced proportionals Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment semicircle shew shewn square on AC tangents THEOR touches the circle triangle ABC twice the rectangle vertex Wherefore