The Elements of Euclid, Viz: 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. the first six books, together with the eleventh and twelfthJ. Nourse, London, and J. Balfour, Edinburgh, 1775 - 520 sider |
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Resultat 1-5 av 38
Side 71
... circle two straight lines cut one another which do not both pass through the center , they do not bi- fect each the other . Let ABCD be a circle , and AC , BD two straight lines in it which cut one another in the point E , and do not ...
... circle two straight lines cut one another which do not both pass through the center , they do not bi- fect each the other . Let ABCD be a circle , and AC , BD two straight lines in it which cut one another in the point E , and do not ...
Side 73
... ABCD be a circle , and AD its diameter , in which let any point F be taken which is not the center : Let the center be E ; of all the straight lines FB , FC , FG , & c . that can be drawn from F to the circumference , FA is the greatest ...
... ABCD be a circle , and AD its diameter , in which let any point F be taken which is not the center : Let the center be E ; of all the straight lines FB , FC , FG , & c . that can be drawn from F to the circumference , FA is the greatest ...
Side 80
... circle ; and , of all others , that which is nearer to the cen ter is always greater than one more remote ; and the greater is nearer to the center than the lefs . Let ABCD be a circle , of which the diameter is AD , and center E ; and ...
... circle ; and , of all others , that which is nearer to the cen ter is always greater than one more remote ; and the greater is nearer to the center than the lefs . Let ABCD be a circle , of which the diameter is AD , and center E ; and ...
Side 85
... circle , and BEC an angle at the center , and Book III . BAC an angle at the circumference , which have the fame cir ... ABCD be a circle , and BAD , BED angles in the fame fegment BAED : The angles BAD , BED are equal to one ...
... circle , and BEC an angle at the center , and Book III . BAC an angle at the circumference , which have the fame cir ... ABCD be a circle , and BAD , BED angles in the fame fegment BAED : The angles BAD , BED are equal to one ...
Side 86
... circle , are together equal to two right angles . Let ABCD be a quadrilateral figure in the circle ABCD ; any two of its opposite angles are together equal to two righe angles . Join AC , BD ; and because the three angles of every tri ...
... circle , are together equal to two right angles . Let ABCD be a quadrilateral figure in the circle ABCD ; any two of its opposite angles are together equal to two righe angles . Join AC , BD ; and because the three angles of every tri ...
Andre utgaver - Vis alle
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Robert Simson Uten tilgangsbegrensning - 1762 |
The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ... Robert Simson Uten tilgangsbegrensning - 1827 |
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Robert Simson Uten tilgangsbegrensning - 1781 |
Vanlige uttrykk og setninger
alfo alſo angle ABC angle BAC bafe baſe BC is equal BC is given becauſe the angle becauſe the ratio biſected Book XI cafe cauſe circle ABCD circumference cone confequently conſtruction cylinder demonſtration deſcribed diameter drawn EFGH equal angles equiangular equimultiples Euclid exceſs fame multiple fame ratio fame reaſon fides fides BA 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 line BC oppoſite parallel parallelepipeds parallelogram paſs perpendicular priſm proportionals propoſition pyramid Q. E. D. PROP rectangle contained rectilineal figure right angles ſame ſecond ſegment ſhall ſhewn ſide ſolid ſpace ſphere ſquare of AC THEOR theſe thoſe triangle ABC vertex wherefore
Populære avsnitt
Side 32 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Side 165 - 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.
Side 170 - 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.
Side 10 - When several angles are at one point B, any ' one of them is expressed by three letters, of which ' the letter that is at the vertex of the angle, that is, at ' the point in which the straight lines that contain the ' angle meet one another, is put between the other two ' letters, and one of these two is...
Side 55 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Side 32 - ... then shall the other sides 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, BCA equal to the angles DEF, EFD, viz.
Side 45 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Side 211 - AB shall be at right angles to the plane CK. Let any plane DE pass through AB, and let CE be the common section of the planes DE, CK ; take any point F in CE, from which draw FG in the plane DE at right D angles to CE ; and because AB is , perpendicular to the plane CK, therefore it is also perpendicular to every straight line in that plane meeting it (3.
Side 38 - F, which is the common vertex of the triangles ; that is, together with four right angles. Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Side 304 - Thus, if B be the extremity of the line AB, or the common extremity of the two lines AB, KB, this extremity is called a point, and has no length : For if it have any, this length must either be part of the length of the line AB, or of the line KB.