The Elements of EuclidLongmans, Green and Company, 1866 - 376 páginas |
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Página 45
... shewn to be equilateral ; therefore it is a square ( Dɛf . 30 ) , and it is described upon the given straight line AB . Q. E. F. COR . Hence every parallelogram that has one right angle has all its angles right angles . PROP . XLVII ...
... shewn to be equilateral ; therefore it is a square ( Dɛf . 30 ) , and it is described upon the given straight line AB . Q. E. F. COR . Hence every parallelogram that has one right angle has all its angles right angles . PROP . XLVII ...
Página 50
... shewn that DE is equal to DG ; therefore DF is equal to DG . Now , the square on CD is equal to the squares on CF , DF , and also equal to the squares on CG , DG ; hence , as DF is equal to DG , CF must be equal to CG ; and , therefore ...
... shewn that DE is equal to DG ; therefore DF is equal to DG . Now , the square on CD is equal to the squares on CF , DF , and also equal to the squares on CG , DG ; hence , as DF is equal to DG , CF must be equal to CG ; and , therefore ...
Página 52
... shew that there may , according to circumstances , be two solutions , one , or none . 7. Describe a circle which shall pass through two given points , and have its centre in a given line . 8. From two given points on the same side of 52 ...
... shew that there may , according to circumstances , be two solutions , one , or none . 7. Describe a circle which shall pass through two given points , and have its centre in a given line . 8. From two given points on the same side of 52 ...
Página 53
... shew that DF , BF ( drawn to a point F within the triangle ABC but not from the ex- tremities of the base ) are together greater than AC , BC . 11. The difference of any two sides of a triangle is less than the third side . 12. Let AB ...
... shew that DF , BF ( drawn to a point F within the triangle ABC but not from the ex- tremities of the base ) are together greater than AC , BC . 11. The difference of any two sides of a triangle is less than the third side . 12. Let AB ...
Página 55
... shew that , according as A and B lie on the same or opposite sides of the line , CF is equal to the semi - sum or semi - difference of AD and BE . 36. Through a given point between two given lines draw a line , such that the parts ...
... shew that , according as A and B lie on the same or opposite sides of the line , CF is equal to the semi - sum or semi - difference of AD and BE . 36. Through a given point between two given lines draw a line , such that the parts ...
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