The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The first six books, together with the eleventh and twelfth |
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Σελίδα 24
Book 1 . Re 4. I. For if it be not greater , it must either be equal to it , or less . but
the angle BAC is not equal to the angle ... F two triangles have two angles of one
equal to two angles of the other ; each to each , and one side equal to one side ...
Book 1 . Re 4. I. For if it be not greater , it must either be equal to it , or less . but
the angle BAC is not equal to the angle ... F two triangles have two angles of one
equal to two angles of the other ; each to each , and one side equal to one side ...
Σελίδα 31
I. gles , each to each , to which the equal fides are opposite . there- Book I. fore
the angle ACB is equal to the angle ... BC meets the ' two straight lines AC , BD
and makes , the alternate angles ACB , CBD equal to one another , AC is parallel
c ...
I. gles , each to each , to which the equal fides are opposite . there- Book I. fore
the angle ACB is equal to the angle ... BC meets the ' two straight lines AC , BD
and makes , the alternate angles ACB , CBD equal to one another , AC is parallel
c ...
Σελίδα 97
14 1 quadrilateral figure AMBK are equal to four right angles , for it Book IV . can
be divided into two triangles ; and that two of them KAM , KBM are right angles ,
the other two AKB , AMB are equal to two right angles . but the L angles DEG ...
14 1 quadrilateral figure AMBK are equal to four right angles , for it Book IV . can
be divided into two triangles ; and that two of them KAM , KBM are right angles ,
the other two AKB , AMB are equal to two right angles . but the L angles DEG ...
Σελίδα 192
Let two planes AB , BC cut one another , and let the line DB be their common
section ; DB is a straight line . ... angle AEG is equal to the angle BEH ~ ;
therefore the triangles AEG , BEH have two angles of one equal to two angles of
the other ...
Let two planes AB , BC cut one another , and let the line DB be their common
section ; DB is a straight line . ... angle AEG is equal to the angle BEH ~ ;
therefore the triangles AEG , BEH have two angles of one equal to two angles of
the other ...
Σελίδα 236
... angle . for the same reason , DEM is a right angle , and is therefore equal to the
angle ABH . and the angle HAB is equal to the angle MDE . therefore in the two
triangles HAB , MDE there are two angles in one equal to two angles in the other
...
... angle . for the same reason , DEM is a right angle , and is therefore equal to the
angle ABH . and the angle HAB is equal to the angle MDE . therefore in the two
triangles HAB , MDE there are two angles in one equal to two angles in the other
...
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Δεν εντοπίσαμε κριτικές στις συνήθεις τοποθεσίες.
Συχνά εμφανιζόμενοι όροι και φράσεις
added alſo altitude angle ABC angle BAC baſe becauſe Book Book XI caſe circle circle ABCD circumference common cone cylinder Definition demonſtrated deſcribed diameter divided double draw drawn equal equal angles equiangular equimultiples exceſs fame fides firſt folid fore four fourth given angle given in poſition given in ſpecies given magnitude given ratio given ſtraight line greater Greek half join leſs likewiſe magnitude manner meet muſt oppoſite parallel parallelogram perpendicular plane priſm produced PROP proportionals Propoſition pyramid radius reaſon rectangle rectangle contained remaining right angles ſame ſecond ſegment ſhall ſhewn ſides ſimilar ſolid ſphere ſquare ſquare of AC taken THEOR theſe third thro triangle ABC wherefore whole
Δημοφιλή αποσπάσματα
Σελίδα 157 - D ; wherefore the remaining angle at C is equal to the remaining angle at F ; Therefore the triangle ABC is equiangular to the triangle DEF. Next, let each of the angles at C, F be not less than a right angle ; the triangle ABC is also, in this case, equiangular to the triangle DEF.
Σελίδα 24 - ... be equal, each to each ; and also the third angle of the one to the third angle of the other. Let ABC, DEF be two triangles which have the angles ABC, ECA equal to the angles DEF, EFD, viz.
Σελίδα 45 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Σελίδα 73 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of...
Σελίδα 163 - 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 81 - ELF. Join BC, EF ; and because the circles ABC, DEF are equal, the straight lines drawn from their centres are equal: therefore the two sides BG, GC, are equal to the two EH, HF ; and the angle at G is equal to the angle at H ; therefore the base BC is equal (4.
Σελίδα 323 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
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 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.
Πληροφορίες βιβλιογραφίας
| Τίτλος | The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The first six books, together with the eleventh and twelfth The Elements of Euclid: Also the Book of Euclid's Data ...cor. Viz. The First Six Books, Together with the Eleventh and Twelfth, Robert Simson |
| Συγγραφέας | Robert Simson |
| Εκδότης | F. Wingrave, 1804 |
| Πρωτότυπο από | το Πανεπιστήμιο του Μίτσιγκαν |
| Ψηφιοποιήθηκε στις | 11 Ιουν. 2007 |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |