## Popular Astronomy, Volume 8; Volume 1900Goodsell Observatory of Carleton College, 1900 |

### From inside the book

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Page 8

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**NON**-**EUCLIDEAN GEOMETRY**. * GEORGE BRUCE HALSTED . " Projective Geometry proper , " says Russell , " does not employ the conception of magnitude . " Now it is in metrical properties alone that non - Euclidean and Euclidean spaces ... Page 9

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**geometry**, which has no refer- ence to quantity , is necessarily true of any form of externality . In metrical**geometry**is an empirical element , arising out of the alternatives of**Euclidean**and**non**-**Euclidean**space . " One of the most ... Page 10

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**Euclid**had used unconsciously , or at least without specific mention ; Rie- mann ...**non**-**Euclidean**systems of his son János , referring to the approximate ...**geometry**, the existence of a case of which independently of parallels was ... Page 11

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**non**-**Euclidean geometry**. An Italian Jesuit , P. Manganotti , discovered that one of his order , the Italian Jesuit Saccheri , had already in 1733 published a series of theorems which the world had been ascribing to Bolyai . Thereupon ... Page 12

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**non**-**Euclidean geometry**. In 1893 , at the International Mathematical Congress at Chi- cago , in the discussion which followed my lecture , ' Some Salient Points in the History of Non - Euclidean and Hyper - Spaces , ' wherein I gave ...### Other editions - View all

### Common terms and phrases

Algol Allegheny Observatory angle aperture appear astronomical Astrophysical axis bright Ceti chart circle clouds College comet coördinates corona craters curve Cygni determined diameter Director disc discovery distance double stars Earth ephemeris equator equatorial Eros Euclid exposure faint geometry give given Greenwich Harvard College Observatory Herculis hour hour angle inches instrument interest July Jupiter lens Leonids Lick Observatory light magnitude Mars means measures Mercury meridian meteors micrometer minima minutes Moon Moon's motion nebula night non-Euclidean geometry object observations obtained orbit parallax period perpendicular photographic planet plate polar POPULAR ASTRONOMY position Professor Keeler published reflector refractor right ascension satellite Saturn seen Sept shadow bands solar solar eclipse spectra spectroscopic spectrum SS Cygni straight Sun's surface telescope tion total eclipse triangle University VARIABLE STARS Venus visible Yerkes Yerkes Observatory