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 38.
Σελίδα 7
But ( Const . ) DA , DB , parts of these equals , are equal . Therefore the remainder AL is equal ( 4x . 3 ) to the re- mainder BG . But it has been shown that BC is equal to BG . Wherefore AL and BC are each of them equal to BG ...
But ( Const . ) DA , DB , parts of these equals , are equal . Therefore the remainder AL is equal ( 4x . 3 ) to the re- mainder BG . But it has been shown that BC is equal to BG . Wherefore AL and BC are each of them equal to BG ...
Σελίδα 13
In like manner it may be shown that no other straight line but BD can be in the same straight line with BC . Therefore BD is in the same straight line with CB . Wherefore , if at a point , & c . Q. E. D. C B PROP . XV . ( THEOREM . ) ...
In like manner it may be shown that no other straight line but BD can be in the same straight line with BC . Therefore BD is in the same straight line with CB . Wherefore , if at a point , & c . Q. E. D. C B PROP . XV . ( THEOREM . ) ...
Σελίδα 15
And it has been shown that AC is not equal to AB . fore the side AC is greater than the side A B. angle , & c . Q. E.D. There- Wherefore the greater PROP . XX . ( THEOREM . ) - Any two sides of a triangle ( ABC ) are together greater ...
And it has been shown that AC is not equal to AB . fore the side AC is greater than the side A B. angle , & c . Q. E.D. There- Wherefore the greater PROP . XX . ( THEOREM . ) - Any two sides of a triangle ( ABC ) are together greater ...
Σελίδα 16
But it has been shown that B A , AC are greater than BE , EC . Much more then are BA , AC , greater than BD , DC . B To each of these AC , are greater A E Again , the exterior angle BDC of the triangle CDE is greater than its interior ...
But it has been shown that B A , AC are greater than BE , EC . Much more then are BA , AC , greater than BD , DC . B To each of these AC , are greater A E Again , the exterior angle BDC of the triangle CDE is greater than its interior ...
Σελίδα 17
Again , the angle BAC is not less than the angle EDF , because then the base BC would be less ( I. 24 ) than the base EF : but it is ( Hyp . ) not less . There- fore the angle BAC is not less than the angle EDF . And it was shown than ...
Again , the angle BAC is not less than the angle EDF , because then the base BC would be less ( I. 24 ) than the base EF : but it is ( Hyp . ) not less . There- fore the angle BAC is not less than the angle EDF . And it was shown than ...
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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 |