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1564 Oct. 20 mane, distantia inter Saturnum et Jovem.

1. Posito transversario in loco stato qui est partium 3500, reperi punctarum in transversario, a se invicem elongationem 1162, quibus juxta operationem proveniunt 398$14⁄35$ cui numero in tabula gnomonica competunt 18 gr. 21 m. distantia syderum quæsita.

2. Collocato eodem in puncto 3700 pinnularum distantia reperiebatur 1233 quibus juxta operationem debentur 399$33⁄37$ hisqve ex tabula respondent gradus ut antea, sed minuta numero 25 fere. Discrepat itaqve observatio in 3 [sic] tantum circiter minutis, quod admodum parum est. Erat autem sine dubio vera distantia 18g 22′ infallibiliter. Stadius distantiam ponit 1818g 8, differentia 0g 14′ parva (tantum erroris facit, amborum semidiameter additus 0g 8 ita 6). Qvam Carellus constituit 15g 20′ diff. 3g 2′ Magna.

The above observations are calculated by the rule of Gemma Frisius (De Radio astronomico et geometrico liber, Antwerp, 1545, cap. 15): Multiplico igitur maximum tabulæ numerum, nempe 1200 per pinnularum interstitium, producuntur autem. . ., atqve hunc numerum divido per transversarii locum. In the first observation  = 398$14⁄35$; Gemma's Tabula gnomonica G. Peurbachii then gives the required angle thus:—

In the Danske Magazin, 4th Series, vol. ii. p. 32, the Rev. Dr. Rördam has communicated a list of Tycho Brahe's pupils, found on a loose sheet of paper (without heading or other description) in the Royal Library of Copenhagen. The handwriting seems to be that of Johannes