The elements of plane geometry; or, The first six books of Euclid, ed. by W. Davis |
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Αποτελέσματα 1 - 5 από τα 20.
Σελίδα 10
to AD in the triangle ACD , the angle ACD is equal ( I. 5 ) to the angle ADC . But the angle ACD is greater ( Ax . 9 ) than the angle BCD . Therefore the angle ADC is also greater than the angle BC D. Much more , then , is the angle BDC ...
to AD in the triangle ACD , the angle ACD is equal ( I. 5 ) to the angle ADC . But the angle ACD is greater ( Ax . 9 ) than the angle BCD . Therefore the angle ADC is also greater than the angle BC D. Much more , then , is the angle BDC ...
Σελίδα 11
to CB , and CD common to the two triangles ACD , BCD , the two sides AC , CD , are equal to the two sides BC , CD , each to each ; and the angle ACD is equal ( Const . ) to the angle BCD . Therefore the base AD is equal to the base ...
to CB , and CD common to the two triangles ACD , BCD , the two sides AC , CD , are equal to the two sides BC , CD , each to each ; and the angle ACD is equal ( Const . ) to the angle BCD . Therefore the base AD is equal to the base ...
Σελίδα 14
two angles AED , DEB , these angles are together equal ( I. 13 ) to two right angles . But the two angles CEA ... In the same manner it can be demonstrated that the angle CEB is equal to the angle AED . ... Q. E. D. B C D PROP . XVIII .
two angles AED , DEB , these angles are together equal ( I. 13 ) to two right angles . But the two angles CEA ... In the same manner it can be demonstrated that the angle CEB is equal to the angle AED . ... Q. E. D. B C D PROP . XVIII .
Σελίδα 15
But the angle BCD is greater ( Ax . 9 ) than the angle ACD : therefore the angle BCD is greater than the angle ADC . But because the angle BCD of the triangle DCB is greater than its angle BDC , and the greater ( I. 19 ) angle is ...
But the angle BCD is greater ( Ax . 9 ) than the angle ACD : therefore the angle BCD is greater than the angle ADC . But because the angle BCD of the triangle DCB is greater than its angle BDC , and the greater ( I. 19 ) angle is ...
Σελίδα 21
A in the straight line AD , make ( I. 23 ) the angle DAE equal to the angle ADC . ... But all the angles of these triangles are equal to the interior angles of the figure , viz . , ABC , BCD , & c . , together with the angles at the ...
A in the straight line AD , make ( I. 23 ) the angle DAE equal to the angle ADC . ... But all the angles of these triangles are equal to the interior angles of the figure , viz . , ABC , BCD , & c . , together with the angles at the ...
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The Elements of Plane Geometry; Or, the First Six Books of Euclid. From the ... Πλήρης προβολή - 1863 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABC is equal ABCD alternate angle ABC angle BAC angle BCD base base BC bisected centre circle ABC circumference common described divided double draw drawn equal angles equal Ax equal Const equiangular equimultiples exterior angle extremities fore fourth given given straight line greater greater ratio half impossible inscribed interior join less magnitudes manner meet multiple opposite angle parallel parallelogram pass perpendicular PROBLEM.)-To produced proportionals proved Q. E. D. PROP reason rectangle rectangle contained rectilineal figure remaining angle right angles segment shown side BC sides similar square square of AC straight line AC Take taken THEOREM.)-If third touches the circle triangle ABC unequal Wherefore
Δημοφιλή αποσπάσματα
Σελίδα 3 - A plane superficies is that in which any two points being taken, the straight line between them lies wholly in that superficies. VIII. A plane angle is the inclination of two lines to one another in a plane, which meet together, but are not in the same direction.
Σελίδα 4 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another : XVI.
Σελίδα 67 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...
Σελίδα 12 - 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.
Σελίδα 93 - From this it is manifest, that the perpendicular drawn from the right angle of a right-angled triangle to the base, is a mean proportional between the segments of the base; and also that each of the sides is a mean proportional between the base, and...
Σελίδα 68 - This word is used when there are four proportionals, and it is inferred that the first has the same ratio to the third which the second has to the fourth ; or that the first is to the third as the second to the fourth : as is shown in Prop.
Σελίδα 5 - LET it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 88 - From this it is plain, that triangles and parallelograms that have equal altitudes, are to one another as their bases. Let the figures be placed so as to have their bases in the same straight line; and having drawn perpendiculars from the vertices of the triangles to the bases, the straight line which joins the vertices is parallel to that in which their bases are, (I.
Σελίδα 69 - This term is used when the first magnitude is to the second of the first rank, as the last but one is to the last of the second rank; and as the second is to the third of the first rank, so is the last but two to the last but one of the second rank; and as the third is to the fourth of the first rank, so is the third from the last to the last but two of the second rank; and so on in a cross order: and the inference is as in the 18th definition.
Σελίδα 21 - ... figure, together with four right angles, are equal to twice as many right angles as the figure has be divided into as many triangles as the figure has sides, by drawing straight lines from a point F within the figure to each of its angles.
Πληροφορίες βιβλιογραφίας
| Τίτλος | The elements of plane geometry; or, The first six books of Euclid, ed. by W. Davis |
| Συγγραφέας | Euclides |
| Επιμελητής | William Davis (B.A.) |
| Εκδόθηκε | 1863 |
| Πρωτότυπο από | Πανεπιστήμιο Οξφόρδης |
| Ψηφιοποιήθηκε στις | 21 Νοεμ. 2006 |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |