Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids; to which are Added, Elements of Plane and Spherical TrigonometryW.E. Dean, 1836 - 311 páginas |
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Página 1
... greater than a part of it ; or , the whole is equal to all its parts taken together ; or , two quantities that are each of them equal to a third quantity , are equal to each other . 5. A Theorem is a demonstrative proposition ; in which ...
... greater than a part of it ; or , the whole is equal to all its parts taken together ; or , two quantities that are each of them equal to a third quantity , are equal to each other . 5. A Theorem is a demonstrative proposition ; in which ...
Página 5
... greater than a right angle . 9. An acute angle is that which is less than a right angle . 10. A figure is that which is enclosed by one or more boundaries . — The word area denotes the quantity of space contained in a figure , without ...
... greater than a right angle . 9. An acute angle is that which is less than a right angle . 10. A figure is that which is enclosed by one or more boundaries . — The word area denotes the quantity of space contained in a figure , without ...
Página 8
... greater than any of its parts . 10. The whole is equal to the sum of all its parts . 11. All right angles are equal to one another . 12. " Two straight lines which intersect one another , cannot be both " rallel to the same straight ...
... greater than any of its parts . 10. The whole is equal to the sum of all its parts . 11. All right angles are equal to one another . 12. " Two straight lines which intersect one another , cannot be both " rallel to the same straight ...
Página 11
... greater than the other : Let AB be the greater , and from it cut off DB equal to AC the less , and join DC ; therefore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two sides DB , BC are equal to ...
... greater than the other : Let AB be the greater , and from it cut off DB equal to AC the less , and join DC ; therefore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two sides DB , BC are equal to ...
Página 13
... greater , which is impossible ; therefore BE is not in the same straight line with BC . And in like manner , it may ... greater than either of the interior , and opposite angles . Let ABC be a triangle , and let its side BC be produced ...
... greater , which is impossible ; therefore BE is not in the same straight line with BC . And in like manner , it may ... greater than either of the interior , and opposite angles . Let ABC be a triangle , and let its side BC be produced ...
Otras ediciones - Ver todas
Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Vista de fragmentos - 1836 |
Términos y frases comunes
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angles equal base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated diameter divided draw Prob equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROP proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore