The Analyst Or a Discourse Addressed to An Infidel Mathematician Wherein It I
The Analyst Or a Discourse Addressed to An Infidel Mathematician Wherein It I
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The right Line C c being produced to K y there are formed three fmall Triangles, the Rectilinear CEc, the Mixtilinear CEc, and the Reftilinear Triangle GET. It is evident thefe three Triangles are dif- ferent from each other, the Rectilinear CEc being lefs than the Mixtilinear CEc, whofe Sides are the three Incre- ments abovementioned, and this ftill lefs than the Triangle CE ?. It is fuppofed that the Ordinate b c moves into the place BC, fo that the Point c is coincident with the Point C s an...d the right Line C E 4.
THE ANALYST.
and confequently the Curve C c, is coin- cident with the Tangent C H. In which cafe the mixtilinear evanefcent Triangle CE c will, in its lafl form, be fimilar to the Triangle GET: And its evanefcent Sides C E, E r, and C c will be porpor- tional to CE, E T, and C? the Sides of the Triangle C E f. And therefore it is concluded, that the Fluxions of the Lines AB, BC, and AC, being in the laft Ratio of their evanefcent Increments, are proportional to the Sides of the Tri- angle C E T, or, which is all one, of the Triangle V E C fimilar thereunto, * It it particularly remarked and infifted ort by the great Author, that the Points C and c muft not be diftant one from ano- ther, by any the lead Interval whatfoever; But that, in order to find the ultimate Proportions of the Lines C E, EC, and C c (/.
What to read after The Analyst Or a Discourse Addressed to An Infidel Mathematician Wherein It I?
You can find similar books in the "Read Also" column, or choose other free books by Berkeley, George, 1685-1753 to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
The right Line C c being produced to K y there are formed three fmall Triangles, the Rectilinear CEc, the Mixtilinear CEc, and the Reftilinear Triangle GET. It is evident thefe three Triangles are dif- ferent from each other, the Rectilinear CEc being lefs than the Mixtilinear CEc, whofe Sides are the three Incre- ments abovementioned, and this ftill lefs than the Triangle CE ?. It is fuppofed that the Ordinate b c moves into the place BC, fo that the Point c is coincident with the Point C s an...d the right Line C E 4.
THE ANALYST.
and confequently the Curve C c, is coin- cident with the Tangent C H. In which cafe the mixtilinear evanefcent Triangle CE c will, in its lafl form, be fimilar to the Triangle GET: And its evanefcent Sides C E, E r, and C c will be porpor- tional to CE, E T, and C? the Sides of the Triangle C E f. And therefore it is concluded, that the Fluxions of the Lines AB, BC, and AC, being in the laft Ratio of their evanefcent Increments, are proportional to the Sides of the Tri- angle C E T, or, which is all one, of the Triangle V E C fimilar thereunto, * It it particularly remarked and infifted ort by the great Author, that the Points C and c muft not be diftant one from ano- ther, by any the lead Interval whatfoever; But that, in order to find the ultimate Proportions of the Lines C E, EC, and C c (/.
What to read after The Analyst Or a Discourse Addressed to An Infidel Mathematician Wherein It I?
You can find similar books in the "Read Also" column, or choose other free books by Berkeley, George, 1685-1753 to read onlineMoreLess
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