The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The first six books, together with the eleventh and twelfthF. Wingrave, 1804 |
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Σελίδα 3
... thro ' the center , See N. and terminated both ways by the circumference . XVIII . A femicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter . XIX . " A fegment of a circle is the ...
... thro ' the center , See N. and terminated both ways by the circumference . XVIII . A femicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter . XIX . " A fegment of a circle is the ...
Σελίδα 28
... thro ' a given point parallel Lct A be the given point , and BC the given straight line ; it is required to draw a straight line thro ' the point A , parallel to the straight E line BC . AF In BC take any point D , and join AD ; and at ...
... thro ' a given point parallel Lct A be the given point , and BC the given straight line ; it is required to draw a straight line thro ' the point A , parallel to the straight E line BC . AF In BC take any point D , and join AD ; and at ...
Σελίδα 29
... thro ' the given point A parallel to the given straight line Book I. BC . Which was to be done . PROP . XΧΧΙΙ . ΤΗHEOR . I F a fide of any triangle be produced , the exterior angle is equal to the two interior and opposite angles ; and ...
... thro ' the given point A parallel to the given straight line Book I. BC . Which was to be done . PROP . XΧΧΙΙ . ΤΗHEOR . I F a fide of any triangle be produced , the exterior angle is equal to the two interior and opposite angles ; and ...
Σελίδα 33
... thro ' B draw BE parallel to CA ; and thro ' C draw CF parallel to BD . therefore each of the B AD C F a . 31. 1 . figures EBCA , DBCF is a parallelogram ; and EBCA is equal to b . 35. 1 . DBCF , because they are upon the fame base BC ...
... thro ' B draw BE parallel to CA ; and thro ' C draw CF parallel to BD . therefore each of the B AD C F a . 31. 1 . figures EBCA , DBCF is a parallelogram ; and EBCA is equal to b . 35. 1 . DBCF , because they are upon the fame base BC ...
Σελίδα 34
... thro ' B draw BG parallel a to CA , and thro ' F draw FH parallel to ED . then each of the figures GBCA , DEFH is a G ADH parallelogram ; and b . 36. I. they are equal to one another , because they are upon equal bafes BC , EF and be- B ...
... thro ' B draw BG parallel a to CA , and thro ' F draw FH parallel to ED . then each of the figures GBCA , DEFH is a G ADH parallelogram ; and b . 36. I. they are equal to one another , because they are upon equal bafes BC , EF and be- B ...
Συχνά εμφανιζόμενοι όροι και φράσεις
alſo altitude angle ABC angle BAC baſe BC BC is equal BC is given becauſe the angle becauſe the ratio biſected Book XI cafe cauſe circle ABCD circumference cone conſtruction cylinder demonſtrated deſcribed diameter drawn EFGH equal angles equiangular equimultiples Euclid exceſs fame multiple fame ratio fame reaſon fides fimilar firſt folid angle fore given angle given in magnitude given in poſition given in ſpecies given magnitude given ratio given ſtraight line gnomon greater join leſs likewife oppoſite parallel parallelepipeds parallelogram paſs perpendicular plane angles priſm PROP proportionals Propoſition pyramid rectangle contained rectilineal figure right angles ſame ſecond ſegment ſhall ſhall be equal ſhewn ſide ſolid ſome ſpace ſphere ſquare of AC ſtraight line AC THEOR theſe thoſe thro triangle ABC vertex wherefore
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 1 - The circumference of every circle is supposed to be divided into 360 equal parts called degrees, and each degree into 60 equal parts called minutes, and each minute into 60 equal parts called seconds, and these into thirds, fourths, &c.
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.