A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes, Exercises and Explanations ... By C. Mansford |
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Página 14
When a straight line standing on another straight line , makes the adjacent angles equal to one another , each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it . 11.
When a straight line standing on another straight line , makes the adjacent angles equal to one another , each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it . 11.
Página 32
To draw a straight line perpendicular to a given straight line of unlimited length , from a given point without it . 1 . Let AB be the given straight line , which may be produced to any length both ways , and let C be a given point ...
To draw a straight line perpendicular to a given straight line of unlimited length , from a given point without it . 1 . Let AB be the given straight line , which may be produced to any length both ways , and let C be a given point ...
Página 33
It is required to draw from a straight line perpendicular to AB . 2 . Take any point D on the other side of AB , and from the centre C , at the distance CD , describe A H the circle EGF , meeting AB in F and G. [ Post . 3. ] ...
It is required to draw from a straight line perpendicular to AB . 2 . Take any point D on the other side of AB , and from the centre C , at the distance CD , describe A H the circle EGF , meeting AB in F and G. [ Post . 3. ] ...
Página 34
In AD take a point E ; join EC and describe an arc cutting the former arc in G. Join CG , which A shall be perpendicular to AB . Join EG and DG . The proof is identical with exercise 2 to prop . 9 . Ex . From a given point to draw a ...
In AD take a point E ; join EC and describe an arc cutting the former arc in G. Join CG , which A shall be perpendicular to AB . Join EG and DG . The proof is identical with exercise 2 to prop . 9 . Ex . From a given point to draw a ...
Página 39
Therefore , any two angles , & c . Q.E.D. Ex . 1. Prove this proposition by joining A to any point E in BC . 2. Only one perpendicular can be drawn from the same point to the same straight line . 3 .
Therefore , any two angles , & c . Q.E.D. Ex . 1. Prove this proposition by joining A to any point E in BC . 2. Only one perpendicular can be drawn from the same point to the same straight line . 3 .
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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 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 |