The Elements of EuclidLongmans, Green and Company, 1866 - 376 páginas |
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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
... half of the parallelogram GBCA , because the 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 ...
... half of the parallelogram GBCA , because the 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 ...
Página 51
... half , CPE , is one - third of a right angle ; also , DPK being a right angle , and CPD two- thirds of a right angle , KPE is two - thirds of a right angle . Again , in the right - angled triangle PCE , the angle CPE being one - third ...
... half , CPE , is one - third of a right angle ; also , DPK being a right angle , and CPD two- thirds of a right angle , KPE is two - thirds of a right angle . Again , in the right - angled triangle PCE , the angle CPE being one - third ...
Página 58
... half that of a parallelo- gram , whose base is the sum of the two parallel sides , and altitude the perpendicular distance between them . 72. On the sides AB , AC of a triangle describe paral- lelograms ABDE , ACFG , and produce DE , FG ...
... half that of a parallelo- gram , whose base is the sum of the two parallel sides , and altitude the perpendicular distance between them . 72. On the sides AB , AC of a triangle describe paral- lelograms ABDE , ACFG , and produce DE , FG ...
Página 59
... half of AC : if through B , C parallel lines be drawn , cutting any other line through A at D , E , then AD is half of AE , and BD of CE , and the triangle ABD a fourth of the triangle ACE ; and , conversely , if BD be such that AD is ...
... half of AC : if through B , C parallel lines be drawn , cutting any other line through A at D , E , then AD is half of AE , and BD of CE , and the triangle ABD a fourth of the triangle ACE ; and , conversely , if BD be such that AD is ...
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