The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected and Some of Euclid's Demonstrations are Restored. Also, The Book of Euclid's Data, in Like Manner Corrected. viz. The first six books, together with the eleventh and twelfth |
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Αποτελέσματα 1 - 5 από τα 10.
Σελίδα 8
Def . is equal to DG , and DA , DB parts of them are equal ; therefore f . 3. Ax . the
remainder AL is equal to the remainder f BG . but it has been fnewn that BC is
equal to BG ; wherefore AL and BC are each of them equal to BG . and things that
...
Def . is equal to DG , and DA , DB parts of them are equal ; therefore f . 3. Ax . the
remainder AL is equal to the remainder f BG . but it has been fnewn that BC is
equal to BG ; wherefore AL and BC are each of them equal to BG . and things that
...
Σελίδα 25
equal to DE , and BC to EF , the two sides GB , BC are equal to Book I. the two
DE , EF , each to each ; and the angle GBC is equal to the angle DEF ; therefore
the base GC is equal a to the base DF , anda . 4. I. the triangle GBC to the
triangle ...
equal to DE , and BC to EF , the two sides GB , BC are equal to Book I. the two
DE , EF , each to each ; and the angle GBC is equal to the angle DEF ; therefore
the base GC is equal a to the base DF , anda . 4. I. the triangle GBC to the
triangle ...
Σελίδα 83
PROP . XXVIII . THEOR . IN N equal circles , equal straight lines cut off equal
circumferences , the greater equal to the greater , and the less to the less . Let
ABC , DEF be equal circles , and BC , EF equal straight lines in them , which cut
off the ...
PROP . XXVIII . THEOR . IN N equal circles , equal straight lines cut off equal
circumferences , the greater equal to the greater , and the less to the less . Let
ABC , DEF be equal circles , and BC , EF equal straight lines in them , which cut
off the ...
Σελίδα 167
figures ABHG , CDEF are equiangular , and have their sides about Book VI . the
equal angles proportionals , they are similar to one another Next , Let it be
required to describe upon a given straight line c.1 . Dcf . 4 . AB , a rectilineal
figure ...
figures ABHG , CDEF are equiangular , and have their sides about Book VI . the
equal angles proportionals , they are similar to one another Next , Let it be
required to describe upon a given straight line c.1 . Dcf . 4 . AB , a rectilineal
figure ...
Σελίδα 184
3 Book VI . the circumference EF , the same multiple is the angle EHN of the
nangle EHF . and if the circumference BL be equal to the circumfe . rence EN ,
the angle BGL is also equal to the angle EHN ; and if the circumference BL be
greater ...
3 Book VI . the circumference EF , the same multiple is the angle EHN of the
nangle EHF . and if the circumference BL be equal to the circumfe . rence EN ,
the angle BGL is also equal to the angle EHN ; and if the circumference BL be
greater ...
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Δεν εντοπίσαμε κριτικές στις συνήθεις τοποθεσίες.
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
added alſo altitude angle ABC angle BAC baſe becauſe Book caſe circle circle ABCD circumference common cone cylinder Definition demonſtrated deſcribed diameter divided double draw drawn equal equal angles equiangular equimultiples exceſs fame fides figure firſt folid angle fore four fourth given angle given in poſition given magnitude given ratio given ſtraight line greater half join leſs likewiſe magnitude manner meet multiple muſt oppoſite parallel parallelogram perpendicular plane produced PROP proportionals Propoſition pyramid radius reaſon rectangle rectangle contained rectilineal remaining right angles ſame ſecond ſegment ſhall ſides ſimilar ſolid ſphere ſquare ſquare of AC taken THEOR theſe third thro triangle ABC wherefore whole
Δημοφιλή αποσπάσματα
Σελίδα 156 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Σελίδα 3 - 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.
Σελίδα 323 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Σελίδα 92 - If from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it ; if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, be equal to the square- of the line which meets it, the line which meets shall touch the circle.
Σελίδα 80 - EA : and because AD is equal to DC, and DE common to the triangles ADE, CDE, the two sides AD, DE are equal to the two CD, DE, each to each ; and the angle ADE is equal to the angle CDE, for each of them is a right angle ; therefore the base AE is equal (4.
Σελίδα 52 - If a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double of the square of half the line bisected, and of the square of the line made up of the half and the part produced.
Σελίδα 36 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Σελίδα 2 - 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 54 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Σελίδα 74 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Πληροφορίες βιβλιογραφίας
| Τίτλος | The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected and Some of Euclid's Demonstrations are Restored. Also, The Book of Euclid's Data, in Like Manner Corrected. viz. The first six books, together with the eleventh and twelfth |
| Συγγραφέας | Robert Simson |
| Εκδότης | A. Foulis, 1781 |
| Πρωτότυπο από | το Πανεπιστήμιο του Μίτσιγκαν |
| Ψηφιοποιήθηκε στις | 11 Ιουν. 2007 |
| Μέγεθος | 466 σελίδες |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |