A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes, Exercises and Explanations ... By C. Mansford1874 |
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Página 15
... which has three equal sides . 25. An isosceles triangle is that which has only two sides equal . 26. A scalene triangle is that which has three unequal sides . 27. A right - angled triangle is that which has DEFINITIONS . 15.
... which has three equal sides . 25. An isosceles triangle is that which has only two sides equal . 26. A scalene triangle is that which has three unequal sides . 27. A right - angled triangle is that which has DEFINITIONS . 15.
Página 18
... unequal . 5. If equals be taken from unequals the remainders are unequal . 6. Things which are double of the same are equal to one another . 7. Things which are halves of the same are equal to one another . 8. Magnitudes which coincide ...
... unequal . 5. If equals be taken from unequals the remainders are unequal . 6. Things which are double of the same are equal to one another . 7. Things which are halves of the same are equal to one another . 8. Magnitudes which coincide ...
Página 26
... unequal to AC , that is , it is equal to it . Therefore , if two angles , & c . Q.E.D. Corollary . Hence every equiangular triangle is also equilateral . If the hypothesis and predicate of a proposition be made to change places , the ...
... unequal to AC , that is , it is equal to it . Therefore , if two angles , & c . Q.E.D. Corollary . Hence every equiangular triangle is also equilateral . If the hypothesis and predicate of a proposition be made to change places , the ...
Página 40
... unequal , the angles opposite to them are unequal ; and the greater side has the greater angle opposite to it . A similar comparison may be made between the 6th and 19th . Ex . Prove this proposition by producing the less side AB to E ...
... unequal , the angles opposite to them are unequal ; and the greater side has the greater angle opposite to it . A similar comparison may be made between the 6th and 19th . Ex . Prove this proposition by producing the less side AB to E ...
Página 50
... unequal to DE , that is , it is equal to it ; and BC is equal to EF ; [ Hyp . ] therefore the two sides AB , BC are equal to the two sides DE , EF , each to each ; and the angle ABC is equal to the angle DEF ; [ Hyp . ] therefore the ...
... unequal to DE , that is , it is equal to it ; and BC is equal to EF ; [ Hyp . ] therefore the two sides AB , BC are equal to the two sides DE , EF , each to each ; and the angle ABC is equal to the angle DEF ; [ Hyp . ] therefore the ...
Otras ediciones - Ver todas
A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes ... Euclides Vista completa - 1874 |
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
ABCD AC is equal alternate angles angle ABC angle ACB angle BAC angle BCD angle EDF angle equal apply axioms base BC bisect BOOK called centre circle coincide common Const construction definitions demonstration describe diagonals diameter difference divided double draw equal sides equilateral triangle Euclid exercise exterior angle fall figure fore geometry given point given rectilineal given straight line gnomon greater Hence isosceles triangle join length less Let ABC meet method namely opposite angle opposite sides parallel parallel to CD parallelogram perpendicular PROBLEM produced prop PROPOSITION proved quadrilateral reason rectangle contained rectilineal figure remainder result right angles side BC sides square on AC Take THEOREM things triangle ABC true truths twice the rectangle unequal units whole
Información bibliográfica
| Título | A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes, Exercises and Explanations ... By C. Mansford |
| Autor | Euclides |
| Editor | Charles MANSFORD |
| Publicado | 1874 |
| Procedencia del original | Biblioteca Británica |
| Digitalizado | 27 Nov. 2020 |
| Exportar cita | BiBTeX EndNote RefMan |