The Elements of EuclidLongmans, Green and Company, 1866 - 376 páginas |
Dentro del libro
Resultados 1-5 de 52
Página 1
... taken , the straight line between them lies wholly in that superficies . VIII , A plane angle is the inclination of two lines to one another in a plane , which meet together , but are not in the same direction . B • IX . A plane ...
... taken , the straight line between them lies wholly in that superficies . VIII , A plane angle is the inclination of two lines to one another in a plane , which meet together , but are not in the same direction . B • IX . A plane ...
Página 5
... taken from equals , the remainders are equal . IV . If equals be added to unequals , the wholes are unequal . V. If equals be taken from unequals , the remainders are unequal . VI . Things that are double of the same thing are equal to ...
... taken from equals , the remainders are equal . IV . If equals be added to unequals , the wholes are unequal . V. If equals be taken from unequals , the remainders are unequal . VI . Things that are double of the same thing are equal to ...
Página 57
... taken , one in each side , the figure formed by joining them will also be a square . 57. Let AD , AE be squares upon the sides of the right - angled triangle ABC , and drop DF , EG , perpendi- culars on the hypotenuse BC produced : then ...
... taken , one in each side , the figure formed by joining them will also be a square . 57. Let AD , AE be squares upon the sides of the right - angled triangle ABC , and drop DF , EG , perpendi- culars on the hypotenuse BC produced : then ...
Página 59
... taken 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 ...
... taken 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 ...
Página 89
... taken in the diameter of a circle equally distant from the centre , the sum of the squares on two lines drawn from these points to any point in the circumference will be constant . 47. The hypotenuse AB of a right - angled triangle ABC ...
... taken in the diameter of a circle equally distant from the centre , the sum of the squares on two lines drawn from these points to any point in the circumference will be constant . 47. The hypotenuse AB of a right - angled triangle ABC ...
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