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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Σελίδα 7
Wherefore CA , AB , BC , are equal to one another ; and therefore 4 . The triangle ABC is equilateral ; and it is described upon the given straight line AB . Which was to be done . PROP . II . - PROBLEM . From a given point to draw a ...
Wherefore CA , AB , BC , are equal to one another ; and therefore 4 . The triangle ABC is equilateral ; and it is described upon the given straight line AB . Which was to be done . PROP . II . - PROBLEM . From a given point to draw a ...
Σελίδα 8
But it has been shown that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore 4 . The straight line AL is equal to BC .
But it has been shown that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore 4 . The straight line AL is equal to BC .
Σελίδα 9
But the point B coincides with the point E ; wherefore the base BC shall coincide with the base EF ; because , the point B coinciding with E , and C with F , if the base BC does not coincide with the base EF , two straight lines would ...
But the point B coincides with the point E ; wherefore the base BC shall coincide with the base EF ; because , the point B coinciding with E , and C with F , if the base BC does not coincide with the base EF , two straight lines would ...
Σελίδα 10
... was proved to be equal to GB ; therefore the two sides BF , FC are equal to the two CG , GB , each to each ; and the angle BFC is equal to the angle CGB , and the base BC is common to the two triangles BFC , CGB ; wherefore ( I. 4. ) ...
... was proved to be equal to GB ; therefore the two sides BF , FC are equal to the two CG , GB , each to each ; and the angle BFC is equal to the angle CGB , and the base BC is common to the two triangles BFC , CGB ; wherefore ( I. 4. ) ...
Σελίδα 11
Wherefore , if two angles , & c . Q.E.D. COR . — Hence every equiangular triangle is also equilateral . PROP . VII . - THEOREM . Upon the same base , and on the same side of it , there cannot be two triangles that have their sides which ...
Wherefore , if two angles , & c . Q.E.D. COR . — Hence every equiangular triangle is also equilateral . PROP . VII . - THEOREM . Upon the same base , and on the same side of it , there cannot be two triangles that have their sides which ...
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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
Πληροφορίες βιβλιογραφίας
| Τίτλος | 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 |
| Συγγραφείς | EUCLID., Samuel A. GOOD |
| Έκδοση | 2 |
| Εκδότης | Charles Henry Law, 1854 |
| Πρωτότυπο από | Η Βρετανική βιβλιοθήκη |
| Ψηφιοποιήθηκε στις | 10 Δεκ. 2013 |
| Μέγεθος | 120 σελίδες |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |