Analysis of information sources in references of the Wikipedia article "Pi" in Portuguese language version.
Sumatur pro ratione radii ad peripheriem, I : πEnglish translation by Ian Bruce Arquivado em 2016-06-10 no Wayback Machine: "π is taken for the ratio of the radius to the periphery [note that in this work, Euler's π is double our π.]"
Denotet 1 : π rationem diametri ad peripheriam
Let 1 : π denote the ratio of the diameter to the circumference)
Ver teorema de Barbier, Corolário 5.1.1, p. 98; triângulos de Reuleaux, pp. 3, 10; curvas suaves como a uma curva analítica devido a Rabinowitz, § 5.3.3, pp. 111–112.
There are various other ways of finding the Lengths, or Areas of particular Curve Lines or Planes, which may very much facilitate the Practice; as for instance, in the Circle, the Diameter is to Circumference as 1 to
3.14159, &c. = π. This Series (among others for the same purpose, and drawn from the same Principle) I receiv'd from the Excellent Analyst, and my much Esteem'd Friend Mr. John Machin; and by means thereof, Van Ceulen's Number, or that in Art. 64.38. may be Examin'd with all desireable Ease and Dispatch.
Reimpresso em Smith, David Eugene (1929). «William Jones: The First Use of π for the Circle Ratio». A Source Book in Mathematics (em inglês). [S.l.]: McGraw–Hill. pp. 346–347
Euler, Leonhard (1755). «§2.2.30». Institutiones Calculi Differentialis (em latim). [S.l.]: Academiae Imperialis Scientiarium Petropolitanae. p. 318. E 212
Euler, Leonhard (1798) [escrito em 1779]. «Investigatio quarundam serierum, quae ad rationem peripheriae circuli ad diametrum vero proxime definiendam maxime sunt accommodatae». Nova Acta Academiae Scientiarum Petropolitinae (em latim). 11: 133–149, 167–168. E 705
Chien-Lih, Hwang (2004). «88.38 Some Observations on the Method of Arctangents for the Calculation of π». Mathematical Gazette (em inglês). 88 (512): 270–278. doi:10.1017/S0025557200175060
Chien-Lih, Hwang (2005). «89.67 An elementary derivation of Euler's series for the arctangent function». Mathematical Gazette (em inglês). 89 (516): 469–470. doi:10.1017/S0025557200178404
δ.π :: semidiameter. semiperipheria
the ratio of the length of a circle to its diameter was represented in the fractional form by the use of two letters [...] J.A. Segner [...] in 1767, he represented 3.14159... by δ:π, as did Oughtred more than a century earlier
Car, soit π la circonference d'un cercle, dout le rayon est = 1
Letting π be the circumference (!) of a circle of unit radius)
Denotet 1 : π rationem diametri ad peripheriam
Let 1 : π denote the ratio of the diameter to the circumference)
Si autem π notet peripheriam circuli, cuius diameter eſt 2
Euler, Leonhard (1755). «§2.2.30». Institutiones Calculi Differentialis (em latim). [S.l.]: Academiae Imperialis Scientiarium Petropolitanae. p. 318. E 212
Euler, Leonhard (1798) [escrito em 1779]. «Investigatio quarundam serierum, quae ad rationem peripheriae circuli ad diametrum vero proxime definiendam maxime sunt accommodatae». Nova Acta Academiae Scientiarum Petropolitinae (em latim). 11: 133–149, 167–168. E 705
Chien-Lih, Hwang (2004). «88.38 Some Observations on the Method of Arctangents for the Calculation of π». Mathematical Gazette (em inglês). 88 (512): 270–278. doi:10.1017/S0025557200175060
Chien-Lih, Hwang (2005). «89.67 An elementary derivation of Euler's series for the arctangent function». Mathematical Gazette (em inglês). 89 (516): 469–470. doi:10.1017/S0025557200178404
It is noticeable that these letters are never used separately, that is, π is not used for 'Semiperipheria'
Car, soit π la circonference d'un cercle, dout le rayon est = 1
Letting π be the circumference (!) of a circle of unit radius)
Ver teorema de Barbier, Corolário 5.1.1, p. 98; triângulos de Reuleaux, pp. 3, 10; curvas suaves como a uma curva analítica devido a Rabinowitz, § 5.3.3, pp. 111–112.
the almost autistic satisfaction of the obsessive-compulsive mathematician fascinated by 'Pi' (which affords the opportunity to hear Bush slowly sing vast chunks of the number in question, several dozen digits long)
It is noticeable that these letters are never used separately, that is, π is not used for 'Semiperipheria'
Car, soit π la circonference d'un cercle, dout le rayon est = 1
Letting π be the circumference (!) of a circle of unit radius)
Euler, Leonhard (1755). «§2.2.30». Institutiones Calculi Differentialis (em latim). [S.l.]: Academiae Imperialis Scientiarium Petropolitanae. p. 318. E 212
Euler, Leonhard (1798) [escrito em 1779]. «Investigatio quarundam serierum, quae ad rationem peripheriae circuli ad diametrum vero proxime definiendam maxime sunt accommodatae». Nova Acta Academiae Scientiarum Petropolitinae (em latim). 11: 133–149, 167–168. E 705
Chien-Lih, Hwang (2004). «88.38 Some Observations on the Method of Arctangents for the Calculation of π». Mathematical Gazette (em inglês). 88 (512): 270–278. doi:10.1017/S0025557200175060
Chien-Lih, Hwang (2005). «89.67 An elementary derivation of Euler's series for the arctangent function». Mathematical Gazette (em inglês). 89 (516): 469–470. doi:10.1017/S0025557200178404
Sumatur pro ratione radii ad peripheriem, I : πEnglish translation by Ian Bruce Arquivado em 2016-06-10 no Wayback Machine: "π is taken for the ratio of the radius to the periphery [note that in this work, Euler's π is double our π.]"
Car, soit π la circonference d'un cercle, dout le rayon est = 1
Letting π be the circumference (!) of a circle of unit radius)
Denotet 1 : π rationem diametri ad peripheriam
Let 1 : π denote the ratio of the diameter to the circumference)
Euler, Leonhard (1755). «§2.2.30». Institutiones Calculi Differentialis (em latim). [S.l.]: Academiae Imperialis Scientiarium Petropolitanae. p. 318. E 212
Euler, Leonhard (1798) [escrito em 1779]. «Investigatio quarundam serierum, quae ad rationem peripheriae circuli ad diametrum vero proxime definiendam maxime sunt accommodatae». Nova Acta Academiae Scientiarum Petropolitinae (em latim). 11: 133–149, 167–168. E 705
Chien-Lih, Hwang (2004). «88.38 Some Observations on the Method of Arctangents for the Calculation of π». Mathematical Gazette (em inglês). 88 (512): 270–278. doi:10.1017/S0025557200175060
Chien-Lih, Hwang (2005). «89.67 An elementary derivation of Euler's series for the arctangent function». Mathematical Gazette (em inglês). 89 (516): 469–470. doi:10.1017/S0025557200178404
Sumatur pro ratione radii ad peripheriem, I : πEnglish translation by Ian Bruce Arquivado em 2016-06-10 no Wayback Machine: "π is taken for the ratio of the radius to the periphery [note that in this work, Euler's π is double our π.]"
Denotet 1 : π rationem diametri ad peripheriam
Let 1 : π denote the ratio of the diameter to the circumference)
the almost autistic satisfaction of the obsessive-compulsive mathematician fascinated by 'Pi' (which affords the opportunity to hear Bush slowly sing vast chunks of the number in question, several dozen digits long)