The Elements of EuclidLongmans, Green and Company, 1866 - 376 páginas |
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Página 3
... semicircle is the figure contained by a dia . meter and the part of the circumference it cuts off . XIX . A segment of a circle is the figure contained by a straight line , and the circumference it cuts off . xx . Rectilineal figures ...
... semicircle is the figure contained by a dia . meter and the part of the circumference it cuts off . XIX . A segment of a circle is the figure contained by a straight line , and the circumference it cuts off . xx . Rectilineal figures ...
Página 78
... semicircle BHF , and produce DE to H , and join GH . A B G E Then , because the straight line BF is divided into two equal parts at G and into two unequal at E , the rectangle BE , EF , together with the square on GE , is equal to the ...
... semicircle BHF , and produce DE to H , and join GH . A B G E Then , because the straight line BF is divided into two equal parts at G and into two unequal at E , the rectangle BE , EF , together with the square on GE , is equal to the ...
Página 82
... semicircle ADB ; draw CD to the circumference , perpendicular to AB ; bisect CB at E , join DE , and produce CB to F , making EF equal to DE : F shall be the point required . B For the rectangle CF , FB to- gether with the square on CE ...
... semicircle ADB ; draw CD to the circumference , perpendicular to AB ; bisect CB at E , join DE , and produce CB to F , making EF equal to DE : F shall be the point required . B For the rectangle CF , FB to- gether with the square on CE ...
Página 84
... semicircle two lines be drawn to the circumference , one to the bisection of the arc , and the other perpendicular to the diameter , then the squares upon these two lines are together double of the square upon the radius . 6. If A be ...
... semicircle two lines be drawn to the circumference , one to the bisection of the arc , and the other perpendicular to the diameter , then the squares upon these two lines are together double of the square upon the radius . 6. If A be ...
Página 85
... semicircle be described , and a perpendicular to the common diameter be drawn , the square on the chord of the greater circle , between the extremity of the diameter and the point of section of the perpendicular , will be double of the ...
... semicircle be described , and a perpendicular to the common diameter be drawn , the square on the chord of the greater circle , between the extremity of the diameter and the point of section of the perpendicular , will be double of the ...
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