A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes, Exercises and Explanations ... By C. Mansford |
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Página ix
The truths to be proved , and the constructions to be made , set forth in general language , form propositions which are either theorems or problems . The former propose something which is to be proved , the latter something to be done ...
The truths to be proved , and the constructions to be made , set forth in general language , form propositions which are either theorems or problems . The former propose something which is to be proved , the latter something to be done ...
Página x
Next follows the construction , directing what lines and circles are to be drawn to aid in the proof of the theorem or the solution of the problem . Lastly comes the demonstration , which shows by a connected course of reasoning that ...
Next follows the construction , directing what lines and circles are to be drawn to aid in the proof of the theorem or the solution of the problem . Lastly comes the demonstration , which shows by a connected course of reasoning that ...
Página 21
As it is , its soliztion requires the description of five circles . The reason of this is also explained on p . 8 . Ex . Show how to produce the less of two lines until it is equal to the greater . PROPOSITION 4. THEOREM .
As it is , its soliztion requires the description of five circles . The reason of this is also explained on p . 8 . Ex . Show how to produce the less of two lines until it is equal to the greater . PROPOSITION 4. THEOREM .
Página 22
THEOREM . A If two triangles have two sides of the one equal to two sides of the other , each to each , and have also the angles contained by those sides equal to one another , they shall also have their bases , or third sides equal ...
THEOREM . A If two triangles have two sides of the one equal to two sides of the other , each to each , and have also the angles contained by those sides equal to one another , they shall also have their bases , or third sides equal ...
Página 23
Q.E.D. The letters Q.E.D. = quod erat demonstrandum , which was to be proved , they are usually added at the close of a theorem . The method of proof here einployed is called proof by ' superposition . Note how carefully Euclid fits one ...
Q.E.D. The letters Q.E.D. = quod erat demonstrandum , which was to be proved , they are usually added at the close of a theorem . The method of proof here einployed is called proof by ' superposition . Note how carefully Euclid fits one ...
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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 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 drawn equal sides equilateral triangle Euclid exercise exterior angle fall figure fore geometry given point given rectilineal given straight line gnomon greater half 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 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 |