## The American Mathematical Monthly: The Official Journal of the Mathematical Association of America, Bind 27Mathematical Association of America, 1920 Includes articles, as well as notes and other features, about mathematics and the profession. |

### Fra bogen

Resultater 1-5 af 100

Side 4

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**Proof**: Let SO2 be perpendicular to 0102 , and let the coördinates of S and S ' be x , y and x ' , y ' respectively and let the radii be p and p ' . Then x = 12 2 y = 2rir2 r1 + r2 ' r2 ( r2 — r1 ) p = ritr2 ( 6 ) and by virtue of ... Side 8

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**Proof**: Let the normal to E1 at 01 and to H2 at O2 intersect at N , and let the intersection of the tangents at these points be T. Let the point of contact of ( 0 ) and ( 01 ) be C1 and of ( 0 ) and ( 02 ) be C2 . Then the angle AO1C1 ... Side 9

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**Proof**: Consider the lines O1N , O2N , 001 , 002. These intersect in the points O and N which are on the tangent to E3 . THEOREM : The axes and normals to two of the conics , together with the tangents to these two conics drawn at the ... Side 10

... and whose radius is the harmonic mean between the radii of the two given circles . 1 In this connection see Steiner , p . 69 and ff .

... and whose radius is the harmonic mean between the radii of the two given circles . 1 In this connection see Steiner , p . 69 and ff .

**Proof**: The center of perspective , P3 , of 10 [ Jan. , WORK OF PAPPUS AND STEINER ON TANGENT CIRCLES . Side 11

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**Proof**: Let there be drawn with T as center and TA as radius a circle . This will pass through C1 and C2 . Therefore C1C2P3 will be the radical axis of the circle just drawn and Cn . The circle with P3 as center and P3A as radius is ...### Andre udgaver - Se alle

### Almindelige termer og sætninger

algebra American Mathematical Society analytic geometry angle application April Association of America calculus Chicago circle circumcenters coefficients College conic construction coördinates course curve derivative determine differential equations discussion E. H. MOORE edition elementary equal formula functions G. A. BLISS G. D. BIRKHOFF given gives Hence high school instructor in mathematics integral intersection J. W. YOUNG L. E. DICKSON logarithms logical mathe Mathematical Association mathematicians MATHEMATICS CLUB mathématiques matics maxima and minima meeting method MONTHLY National Committee nine-point circle orthocentric paper perpendicular physics plane polyconic projection positive present problem Prof professor of mathematics projection proof Proposed r₁ radius result Review roots Section sides solution straight line surface tangent teachers teaching theorem theory tion triangle trigonometry Univ University variable vector vertices volume zero

### Populære passager

Side 409 - Until the phenomena of any branch of knowledge have been submitted to measurement and number it cannot assume the status and dignity of a science.

Side 16 - That, if a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.

Side 191 - our astronomical observer" at a salary of £100 per annum, his duty being " forthwith to apply himself with the most exact care and diligence to the rectifying the tables of the motions of the heavens and the places of the fixed stars, so as to find out the so much desired longitude of places for the perfecting the art of navigation.

Side 104 - Drill in algebraic manipulation should be limited to those processes and to the degree of complexity required for a thorough understanding of principles and for probable applications either in common life or in subsequent courses which a substantial proportion of the pupils will take.

Side 146 - Louis in connection with the meeting of the Department of superintendence of the National education association, February 27-29, 1912.

Side 146 - York (representing the Association of Teachers of Mathematics in the Middle States and Maryland...

Side 191 - Royal was established in 1765, the duty of the incumbent was declared to be " to apply himself with the most exact care and diligence to the rectifying the Tables of the Motions of the Heavens, and the places of the Fixed Stars in order to find out the so much desired Longitude at Sea for the perfecting -the Art of Navigation.

Side 221 - The great attraction of the theory is its logical consistency. If any deduction from it should prove untenable, it must be given up. A modification of it seems impossible without destruction of the whole. No one must think that Newton's great creation can be overthrown in any real sense by this or by any other theory. His clear and wide ideas will for ever retain their significance as the foundation on which our modern conceptions of physics have been built.

Side 52 - The squares on two sides of a triangle are together equal to twice the square on half the third side and twice the square on the median to that side. If ABC be a...

Side 178 - AFTER the lamentable breach in the former international relations existing among men of science, it is with joy and gratefulness that I accept this opportunity of communication with English astronomers and physicists.