To date, Google Books has scanned 50,000 books from the 16th and 17th cenÂturies. And by workÂing with great EuroÂpean libraries (Oxford UniÂverÂsiÂty Library and the NationÂal Libraries of FloÂrence and Rome, to name a few), the MounÂtain View-based comÂpaÂny expects to index hunÂdreds of thouÂsands of pre-1800 titles in the comÂing years.
TraÂdiÂtionÂalÂly, most hisÂtorÂiÂcal texts have been scanned in black & white. But these newÂfanÂgled scans are being made in colÂor, givÂing readÂers anyÂwhere the chance to read oldÂer books “as they actuÂalÂly appear” and to appreÂciÂate the “great flowÂerÂing of experÂiÂmenÂtaÂtion in typogÂraÂphy that took place in the 16th and 17th cenÂturies.”
Some of the founÂdaÂtionÂal texts now availÂable in colÂor include NosÂtradamus’ ProgÂnosÂtiÂcaÂtion nouÂvelle et preÂdicÂtion porÂtenÂteuse (1554), Johannes Kepler’s EpitÂoÂme AstronoÂmiÂae CoperÂniÂcanae from 1635, and Galileo’s SysÂtema cosÂmicum from 1641. All texts can be viewed online, or downÂloaded as a PDF (although the PDF’s lack colÂor)…
RelatÂed ConÂtent:
Google “Art Project” Brings Great PaintÂings & MuseÂums to You
Google to ProÂvide VirÂtuÂal Tours of 19 World HerÂitage Sites
FYI, Galileo’s book is not entiÂtled “SysÂtema CosÂmicum”. It is realÂly the fourth part of “DiaÂlogue ConÂcernÂing Two Chief World SysÂtems”
FYI, Galileo’s book is not entiÂtled “SysÂtema CosÂmicum”. It is realÂly the fourth part of “DiaÂlogue ConÂcernÂing Two Chief World SysÂtems”
Galileo’s law of falling bodÂies v^2=d is the same as Kepler’s disÂtance law v^2=(1/r). The reaÂson for this is that there are two ways of meaÂsurÂing the same velocÂiÂty, disÂtance per unit time and time per unit disÂtance, with one meaÂsure being the recÂiÂpÂroÂcal of the othÂer. In its ellipÂtiÂcal conÂtext r+d equals the major axis a conÂstant.
FurÂther to my preÂviÂous comÂments, the conÂnecÂtion between Galileo’s v^2=d at the empÂty focus end of the ellipÂtiÂcal orbit and Kepler’s v^2=1/r at the Sun focus end is mathÂeÂmatÂiÂcalÂly very interÂestÂing and not at all straight forÂward. Kepler’s verÂsion can be adaptÂed for furÂther research purÂposÂes by includÂing a conÂstatÂnt V being the maxÂiÂmum velocÂiÂty, then the variÂable velocÂiÂties can be expressed as V/#r where # is my notaÂtion for square root. In this way the same velocÂiÂty arisÂes on both the accelÂerÂatÂing side as well as the decelÂerÂatÂing side but in oppoÂsite direcÂtions. As one of the propÂerÂties of all perÂfect ellipses d is the disÂtance from the curve to the empÂty focus, and r is the disÂtance from the curve to the Sun focus. d+r equals the major axis of the ellipÂtiÂcal orbit which I will call A. As a matÂter of furÂther mathÂeÂmatÂiÂcal interÂest A/V equals #(r/d) +#(d/r). Just as the variÂable velocÂiÂties at the Sun focus end can be expressed as V/#r so the variÂable velocÂiÂties at the empÂty focus end can be expressed accordÂing to Galileo’s forÂmuÂla as #d=v where d is the disÂtance from the empÂty focus to either side of the ellipÂtiÂcal curve.
Kepler liked to base his mathÂeÂmatÂiÂcal ideas on the ancient Greeks. This is parÂticÂuÂlarÂly eviÂdent in his litÂtle known paper ConÂcernÂing ConÂic SecÂtions, part of his book on Optics pubÂlished in 1604. Kepler supÂposed that geoÂmetÂric shapes which were conÂic secÂtions would all have focusÂes, a conÂcept which he inventÂed and described as being conÂstructÂed by pins and thread. At first Kepler failed to recogÂnise that foci dependÂed on symÂmeÂtry not conÂic secÂtions, and was thereÂfore comÂpleteÂly wrong about the conÂnecÂtion with conÂic secÂtions. A more symÂmetÂriÂcal shape would be cylinÂdric secÂtion an expresÂsion which Kepler nevÂer uses. HowÂevÂer in 1618 Kepler at last found a conÂstrucÂtive appliÂcaÂtion for the focus nameÂly as the locaÂtion of the Sun in the symÂmetÂriÂcal planÂeÂtary orbits, givÂing rise to Kepler’s disÂtance law which applies throughÂout the whole uniÂverse.
A cylinÂdric secÂtion has two foci (f) which relate to the half axes (a and b) as folÂlows f = a -(a^2 — b^2)^(0.5). Kepler recogÂnised that this forÂmuÂla could probÂaÂbly be conÂstructÂed by pins and thread in his litÂtle known work of 1604. A slightÂly less accuÂrate verÂsion of this forÂmuÂla can be used for ellipses. Very few astronomers seem to be aware that an axis can easÂiÂly be calÂcuÂlatÂed if the othÂer axis and the focus are known.