The Synoptical Euclid; Being the First Four Books of Euclid's Elements of Geometry from the Edition of Dr. Robert Simson ... With Exercises. By S. A. Good ... Second Edition |
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Página 43
Let AB be the given straight line ; it is required to describe a square upon AB . D A B From the point A draw ( I. ll . ) AC at right angles to AB , and make ( I. 3. ) AD equal to AB , and through the point D draw DE parallel ( I. 31. ) ...
Let AB be the given straight line ; it is required to describe a square upon AB . D A B From the point A draw ( I. ll . ) AC at right angles to AB , and make ( I. 3. ) AD equal to AB , and through the point D draw DE parallel ( I. 31. ) ...
Página 44
the square BDEC , and on BA , AC , the squares GB , HC ; through A draw ( I. 31. ) AL parallel to BD , or CE , and join AD , FC . Then , because each of the angles BAC , BAG , is a right angle ( Def . 30. ) , the two straight lines AC ...
the square BDEC , and on BA , AC , the squares GB , HC ; through A draw ( I. 31. ) AL parallel to BD , or CE , and join AD , FC . Then , because each of the angles BAC , BAG , is a right angle ( Def . 30. ) , the two straight lines AC ...
Página 45
The square upon the side BC is equal to the squares upon the sides BĀ , AC . Therefore , in any right - angled triangle , & c . Q.E.D. PROP . XLVIII . - THEOREM . If the square described upon one of the sides of a triangle , be equal to ...
The square upon the side BC is equal to the squares upon the sides BĀ , AC . Therefore , in any right - angled triangle , & c . Q.E.D. PROP . XLVIII . - THEOREM . If the square described upon one of the sides of a triangle , be equal to ...
Página 46
To each of these add the square of AC ; therefore 2 . The squares of DA , AC , are equal to the squares of BA , AC . But ( I. 47. ) 3 . The square of DC is equal to the squares of DA , AC , because DAC is a right angle ; and the square ...
To each of these add the square of AC ; therefore 2 . The squares of DA , AC , are equal to the squares of BA , AC . But ( I. 47. ) 3 . The square of DC is equal to the squares of DA , AC , because DAC is a right angle ; and the square ...
Página 48
the square ADEB , and through C draw . ( I. 31. ) CF parallel to AD or BE. * N.B. ~ To avoid repeating the word contained too frequently , the rectangle contained by two straight lines AB , AC , is sometimes simply called the rectangle ...
the square ADEB , and through C draw . ( I. 31. ) CF parallel to AD or BE. * N.B. ~ To avoid repeating the word contained too frequently , the rectangle contained by two straight lines AB , AC , is sometimes simply called the rectangle ...
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Términos y frases comunes
AB is equal ABC is equal ABCD angle ABC angle ACB angle AGH angle BAC angle BCD angle equal base BC bisected centre circle ABC circumference coincide common demonstrated describe diameter distance divided double draw equal angles exterior angle extremity fall figure four given circle given point given straight line gnomon greater impossible inscribed join less Let ABC Let the straight likewise manner meet opposite angles parallel parallelogram pass pentagon perpendicular point F PROBLEM produced Q.E.D. PROP reason rectangle contained rectilineal figure remaining angle right angles segment semicircle shown side BC sides square of AC straight line AC Take touches the circle triangle ABC twice the rectangle wherefore whole
Información bibliográfica
| Título | The Synoptical Euclid; Being the First Four Books of Euclid's Elements of Geometry from the Edition of Dr. Robert Simson ... With Exercises. By S. A. Good ... Second Edition |
| Autores | EUCLID., Samuel A. GOOD |
| Edición | 2 |
| Editor | Charles Henry Law, 1854 |
| Procedencia del original | Biblioteca Británica |
| Digitalizado | 10 Dic. 2013 |
| Largo | 120 páginas |
| Exportar cita | BiBTeX EndNote RefMan |