A School Euclid. Being Books I. & II. of Euclid's Elements, with Notes, Exercises and Explanations Appended to Each Proposition1875 - 112 páginas |
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Página 9
... bisect a given finite straight line , that is , to divide it into two equal parts . " These statements form what is called the general enunciation of the proposition , after which comes the discussion . First , the general enunciation ...
... bisect a given finite straight line , that is , to divide it into two equal parts . " These statements form what is called the general enunciation of the proposition , after which comes the discussion . First , the general enunciation ...
Página 26
... bisect the angles B and C of an equilateral tri- angle , then OA also bisects the angle A and OA , BO and CO are all equal to one another . PROPOSITION 7. THEOREM . On the same base , and on the same side of it , there cannot be two ...
... bisect the angles B and C of an equilateral tri- angle , then OA also bisects the angle A and OA , BO and CO are all equal to one another . PROPOSITION 7. THEOREM . On the same base , and on the same side of it , there cannot be two ...
Página 29
... bisects each of the angles through which it passes . Hence show that 2. The diagonals of a square bisect each other at right angles . [ Prop . 4. ] PROPOSITION 9. PROBLEM . To bisect a given rectilineal angle BOOK I. 8 . 29.
... bisects each of the angles through which it passes . Hence show that 2. The diagonals of a square bisect each other at right angles . [ Prop . 4. ] PROPOSITION 9. PROBLEM . To bisect a given rectilineal angle BOOK I. 8 . 29.
Página 30
Euclid, Charles Mansford. PROPOSITION 9. PROBLEM . To bisect a given rectilineal angle , that is to divide it into two equal angles . Let BAC be the given recti- 1. lineal angle . It is required to bisect it . 2 . Take any point D in AB ...
Euclid, Charles Mansford. PROPOSITION 9. PROBLEM . To bisect a given rectilineal angle , that is to divide it into two equal angles . Let BAC be the given recti- 1. lineal angle . It is required to bisect it . 2 . Take any point D in AB ...
Página 31
... bisect the angle ACB by the straight line CD . [ I. 9. ] AB shall be cut into two equal A parts at the point D. Because AC is equal to CB [ Def . 24 ] , and CD 3. is common to the two triangles ACD , BCD , the two sides , AC , CD are ...
... bisect the angle ACB by the straight line CD . [ I. 9. ] AB shall be cut into two equal A parts at the point D. Because AC is equal to CB [ Def . 24 ] , and CD 3. is common to the two triangles ACD , BCD , the two sides , AC , CD are ...
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A School Euclid, Being Books I. & II. of Euclid's Elements, with Notes by C ... Euclides Sin vista previa disponible - 2015 |
Términos y frases comunes
AC is equal adjacent angles alternate angles angle ABC angle ACB angle AGH angle BAC angle BCD angle EDF angle equal angles are equal angles CEA axioms base BC BC is equal bisect centre coincide Const diagonals diameter double equal sides equal to BC equal to twice equilateral triangle Euclid exterior angle fore four right angles given point given rectilineal angle given straight line gnomon half a right hypotenuse interior and opposite isosceles triangle join Let ABC Let the straight obtuse opposite angle opposite sides parallel to CD parallelogram parallelogram ABCD perpendicular produced prop quadrilateral rectangle AC rectangle contained remaining angle rhombus right angles right-angled triangle shew side BC sides equal square described square on AC THEOREM third angle triangle ABC triangle DEF truths twice the rectangle unequal