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 twelfthA. Foulis, 1781 - 466 sider |
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Resultat 6-10 av 79
Side 19
... BAC , ACB , as also CAB , ABC are less than two right an- gles . therefore any two angles , & c . Q. E. D. THE PROP . XVIII . THE OR . greater fide of every triangle is opposite to the greater angle . Let ABC be a triangle of which the ...
... BAC , ACB , as also CAB , ABC are less than two right an- gles . therefore any two angles , & c . Q. E. D. THE PROP . XVIII . THE OR . greater fide of every triangle is opposite to the greater angle . Let ABC be a triangle of which the ...
Side 20
... angle ACB ; but it is not ; therefore the fide AC is not lefs than AB . and ... triangle are together greater than the third fide . Let ABC be a triangle ; any ... BAC . Produce BD to E ; and becaufe two fides of a triangle are great- er ...
... angle ACB ; but it is not ; therefore the fide AC is not lefs than AB . and ... triangle are together greater than the third fide . Let ABC be a triangle ; any ... BAC . Produce BD to E ; and becaufe two fides of a triangle are great- er ...
Side 21
... angle of a triangle is greater than the interior and opposite angle , the exterior angle BDC of the tri- angle CDE is greater than CED . for the fame reason , the exterior angle CEB of the triangle ABE is greater than BAC . and it has ...
... angle of a triangle is greater than the interior and opposite angle , the exterior angle BDC of the tri- angle CDE is greater than CED . for the fame reason , the exterior angle CEB of the triangle ABE is greater than BAC . and it has ...
Side 23
... angle BAC greater than the angle EDF . the bafe BC is alfo greater than the bafe EF . Of the two fides DE , DF let DE be the fide which is not greater than the other , and at the point D in the straight line DE a make the angle EDG ...
... angle BAC greater than the angle EDF . the bafe BC is alfo greater than the bafe EF . Of the two fides DE , DF let DE be the fide which is not greater than the other , and at the point D in the straight line DE a make the angle EDG ...
Side 24
... angle BAC is not equal to the angle EDF , because them the bafe BC would be a equal to EF . but it is not ; therefore the angle BAC is not e- qual to the angle EDF . neither is it lefs ; be- cause then the base BC would be lefs b than ...
... angle BAC is not equal to the angle EDF , because them the bafe BC would be a equal to EF . but it is not ; therefore the angle BAC is not e- qual to the angle EDF . neither is it lefs ; be- cause then the base BC would be lefs b than ...
Andre utgaver - Vis alle
The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ... Robert Simson Uten tilgangsbegrensning - 1775 |
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 |
Vanlige uttrykk og setninger
AC is equal alfo alſo angle ABC angle BAC bafe baſe BC is given becauſe the angle bifected Book XI cafe circle ABCD circumference cone confequently cylinder defcribed demonftrated diameter drawn EFGH equal angles equiangular equimultiples Euclid excefs faid fame manner fame multiple fame ratio fecond fegment fhall fhewn fide BC fides fimilar fince firft firſt folid angle fome fore fquare of AC ftraight line AB given angle given ftraight line given in fpecies given in magnitude given in pofition given magnitude given ratio gnomon greater join lefs leſs likewife line BC muſt oppofite parallel parallelepipeds parallelogram perpendicular prifm Propofition proportionals pyramid rectangle contained rectilineal figure right angles ſhall ſphere ſquare thefe THEOR theſe thro tiple triangle ABC vertex wherefore
Populære avsnitt
Side 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.
Side 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.
Side 323 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 74 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...