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[Theoretischer astronomischer Nachlass] (7. Band)

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Public Domain Mark 1.0. You can find more information here.

Bibliographic data

fullscreen: [Theoretischer astronomischer Nachlass] (7. Band)

Multivolume work

Persistent identifier:
1669258823
Title:
Actes du Symposium International de la Commission VII de la Société Internationale de Photogrammétrie et Télédétection
Sub title:
Toulouse, 13 - 17 Septembre 1982
Year of publication:
1982
Place of publication:
Toulouse
Publisher of the original:
[Verlag nicht ermittelbar]
Identifier (digital):
1669258823
Language:
English
Editor:
Laidet, L.
Corporations:
International Society for Photogrammetry and Remote Sensing, Commission VII, Interpretation of Data
Adapter:
International Society for Photogrammetry and Remote Sensing, Commission VII, Interpretation of Data
Founder of work:
International Society for Photogrammetry and Remote Sensing, Commission VII, Interpretation of Data
Other corporate:
International Society for Photogrammetry and Remote Sensing, Commission VII, Interpretation of Data
Document type:
Multivolume work

Volume

Persistent identifier:
1669259897
Title:
Actes du Symposium International de la Commission VII de la Société Internationale de Photogrammétrie et Télédétection
Scope:
XV, 415 Seiten
Year of publication:
1982
Place of publication:
Toulouse
Publisher of the original:
[Verlag nicht ermittelbar]
Identifier (digital):
1669259897
Illustration:
Illustrationen, Diagramme
Signature of the source:
ZS 312(24,7,2)
Language:
English
Additional Notes:
Erscheinungsdatum des Originals ist ermittelt.
Usage licence:
Attribution 4.0 International (CC BY 4.0)
Editor:
Laidet, L.
Corporations:
International Society for Photogrammetry and Remote Sensing,, Commission VII, Interpretation of Data
Adapter:
International Society for Photogrammetry and Remote Sensing,, Commission VII, Interpretation of Data
Founder of work:
International Society for Photogrammetry and Remote Sensing,, Commission VII, Interpretation of Data
Other corporate:
International Society for Photogrammetry and Remote Sensing,, Commission VII, Interpretation of Data
Publisher of the digital copy:
Technische Informationsbibliothek Hannover
Place of publication of the digital copy:
Hannover
Year of publication of the original:
2019
Document type:
Volume
Collection:
Earth sciences

Chapter

Title:
VENDREDI !/ SEPTEMBRE 1983 - FRIDAY SEPTEMBER 17, 1983 9.00 - 10.30 RAPPORTS DES GROUPES DE TRAVAIL - WORKING GROUP REPORTS
Document type:
Multivolume work
Structure type:
Chapter

Section

Title:
RAPPORT DE SYNTHESE DU GROUPE DE TRAVAIL VII-7 W. G. VII-7 Report "OCEANOGRAPHIE ET ZONES COTIERES" - "Oceanography and coastal zone" par / by H. OCHIAI, K. A. ULBRICHT
Document type:
Multivolume work
Structure type:
Section

Contents

Table of contents

  • Werke
  • [Theoretischer astronomischer Nachlass] (7. Band)
  • Cover
  • Title page
  • Title page
  • THEORIA MOTUS CORPORUM COELESTIUM IN SECTIONIBUS CONICIS SOLEM AMBIENTIUM
  • Title page
  • PRAEFATIO.
  • CONTENTA.
  • LIBER PRIMUS. RELATIONES GENERALES INTER QUANTITATES PER QUAS CORPORUM COELESTIUM MOTUS CIRCA SOLEM DEFINIUNTUR.
  • LIBER SECUNDUS. INVESTIGATIO ORBITARUM CORPORUM COELESTIUM EX OBSERVATIONIBUS GEOCENTRICIS.
  • SECTIO PRIMA. Determinatio orbitae e tribus observationibus completis.
  • 115. Ad determinationem completam motus corporis coelestis in orbita sua requiruntur elementa septem, [...]
  • 116. Antequam determinatio alicuius orbitae ex observationibus geocentricis suscipitur, [...]
  • 117. Positio terrae hoc modo e tabulis computata ad terrae centrum referenda est, [...]
  • 118. Si corporis coelestis distantia a terra alicui observationi respondens proxime iam nota est, [...]
  • 119. Haud difficile esset, e nexu inter problematis nostri data atque incognitas, [...]
  • 120. Quoniam itaque problematis natura reductionem ulteriorem non permittit, [...]
  • 121. Quoties itaque incognitarum valores approximati iam in potestate sunt, [...]
  • 122. Quum incognitarum valores in hypothesi secunda et tertia supponendi quodammodo arbitrarii sint, [...]
  • 123. In praec. supposuimus, valores approximatos incognitarum x, y alicunde iam haberi. [...]
  • 124. Progredimur iam ad enumerationem methodorum maxime idonearum principiis praecedentibus innixarum, [...]
  • 125. Levi mutatione applicata e methodo praecedente secundam eliciemus.
  • 126. Methodus praecedens ad tertiam illico sternit viam.
  • 127. Postquam tres loci heliocentrici eo quem in art. praec. descripsimus modo eruti sunt, [...]
  • 128. Designemus tres radios vectores eodem modo erutos ut in artt. 125, 126 per [...]; [...]
  • 129. Quinque methodi hactenus expositae protinus ad totidem alias viam sternunt, [...]
  • 130. Decem methodi inde ab art. 124 explicatae innituntur suppositioni, [...]
  • 131. In art. 114 ostensum est, si ratio inter quantitates illic atque in art 128 per n, n', n'' denotatas cognita fuerit, [...]
  • 132. Statuendo brevitatis gratia (0.1.2)=a, (0.I.2)D'=-b, (0.O.2)D=c, (0. II. 2)D''=d, [...]
  • 133. Quum cosinus angulorum f, f', f", perinde ut quantitates [...] ab unitate differentia secundi ordinis discrepent, [...]
  • 134. Ex praecedentibus iam ratio percipietur, cur in methodo nostra pro x, y resp. quantitates [...]
  • 135. Disquisitiones praecedentes eum in finem allatae sunt, ut principia, [...]
  • 136. Ante omnia tres locos heliocentricos terrae in sphaera coelesti A, A' A" [...]
  • 137. Negotium secundum erit determinatio situs relativi illorum trium circulorum maximorum inter se, [...]
  • 138. Negotium tertium iam in eo consistit, ut duo loci geocentrici extremi corporis coelestis, [...]
  • 139. Sint in sphaera coelesti C, C', C'' tria corporis coelestis loca heliocentrica, [...]
  • 140. Primo observamus, si N fuerit punctum quodcunque circuli maximi C C' C'', [...]
  • 141. Ex [...] atque aequatione III art. praec. sequitur [...]
  • 142. Aequatio IV, quae evoluta ad ordinem octavum ascenderet, [...]
  • 143. Simulac angulus z erutus est, statim habetur [...] per aequationem [...]
  • 144. Arcubus [...] inventis, punctorum C, C" positio data erit, [...]
  • 145. Postquam hoc modo corporis coelestis positiones in orbita determinatae sunt, [...]
  • 146. Calculus elementorum, hinc ex [...], 2f atque temporis intervallo correcto inter observationem secundam et tertiam, [...]
  • 147. Proprie quidem etiam hic, sicuti in decem methodis supra traditis, [...]
  • 148. Quoties elementa e tribus observationibus derivanda adhuc penitus incognita sunt (cui casui methodus nostra imprimis accomodata est), [...]
  • 149. In ultima demum hypothesi elementa ipsa calculabuntur, [...]
  • 150. Progredimur iam ad illustrationem huius methodi per aliquot exempla copiose explicanda, [...]
  • 151. Omnibus hisce reductionibus rite applicatis, [...]
  • 152. Calculis praeliminaribus hoc modo absolutis, [...]
  • 153. In hypothesi secunda ipsis P, Q eos ipsos valores tribuemus, [...]
  • 154. Ne quidquam desiderandum relinquatur, adhuc tertiam hypothesin extruemus, [...]
  • 155. Quo clarius elucescat, quanta praecisione elementa inventa gaudeant, [...]
  • 156. Exemplum secundum a Pallade sumemus, [...]
  • 157. Primo nunc situm circulorum maximorum a locis heliocentricis terrae ad locos geocentricos planetae ductorum determinabimus. [...]
  • 158. Duo exempla praecedentia occasionem nondum suppeditaverunt, [...]
  • 159. Ad exemplum tertium observationes sequentes Cereris eligimus, [...]
  • 160. In expositione methodi, cui disquisitiones praecedentes dicatae fuerunt [...]
  • 161. Casus primi tres subdivisiones faciemus: [...]
  • 162. In casu secundo, ubi B'' cum B coincidit, [...]
  • 163. Methodus, quam inde ab art. 136 exposuimus, [...]
  • SECTIO SECUNDA. Determinatio orbitae e quatuor observationibus, quarum duae tantum completae sunt.
  • SECTIO TERTIA. Determinatio orbitae observationibus quotcunque quam proxime satisfacientis.
  • SECTIO QUARTA. De determinatione orbitarum, habita ratione perturbationum.
  • TABULAE.
  • BEMERKUNGEN.
  • ZUSÄTZE ZUR THEORIA MOTUS CORPORUM COELESTIUM UND ANDERE NACHTRÄGE ZUR ELLIPTISCHEN BEWEGUNG.
  • ZUR PARABOLISCHEN BEWEGUNG.
  • STÖRUNGEN DER CERES.
  • STÖRUNGEN DER PALLAS.
  • THEORIE DER BEWEGUNG DES MONDES.
  • BERICHTIGUNGEN UND ZUSÄTZE.
  • BEMERKUNGEN ZUM SIEBENTEN BANDE.
  • INHALT. GAUSS WERKE BAND VII. THEORETISCHE ASTRONOMIE.
  • Cover

Full text

188 
THEORIA MOTUS CORPORUM COELESTIUM. LIBER II. SECTIO I. 
dein 
n'r' 
n 
sms 
sine' 
• sin [z -(- A'D - 
-b' 
n'r' 
sin e " 
• sin (e + A'D" 
-b 
n" 
sine' 
*(V—0 = ? 
n tr ff a \ „ H 
X (X p - 1) = q 
eliciemus C et r ex rsinC=jo, rcosC = q, atque C' et r" ex r"sinC' = p", 
r" cos C," = q". Ambiguitas in determinandis C et C hic adesse nequit, quia r 
et r" necessario evadere debent quantitates positivae. Calculus perfectus per 
aequationem VII si lubet confirmari poterit. 
Sunt tamen duo casus, ubi aliam methodum sequi oportet. Quoties sci 
licet punctum D' cum B vel coincidit vel ipsi in sphaera oppositum est, 
sive quoties AD'—b = 0 vel = 180°, aequationes VI et IX necessario identi- 
cae esse debent, fieretque x = oo, ~kp —1 = 0, adeoque q indeterminata. In 
hoc casu C et r" quidem eo quo docuimus modo determinabuntur, dein vero 
C et r e combinatione aequationis VII cum VI vel IX elicere oportebit. For 
mulas ipsas ex art. 7 8 desumendas huc transscribere supersedemus; observa 
mus tantummodo, quod in eo quoque casu, ubi est AD — b non quidem = 0 
neque = 180°, attamen arcus valde parvus, eandem methodum sequi praestat, 
quoniam tunc methodus prior praecisionem necessariam non admitteret. Et 
quidem adoptabitur combinatio aequationis VII cum VI vel cum IX, prout 
sin (AD"-AD') maior vel minor est quam sin (AD"—8). 
Perinde in casu, ubi punctum D', vel ipsi oppositum, cum B" vel coin 
cidit vel parum ab eodem distat, determinatio ipsarum C", r" per methodum 
praecedentem vel impossibilis vel parum tuta foret. Tunc itaque C et r qui 
dem per illam methodum determinabuntur, dein vero C et r" e combinatione 
aequationis VII vel cum V vel cum VIII, prout sin [A'D — A"D') maior vel 
minor est quam sin(A"D — 8"). Ceterum haud metuendum est, ne simul D' 
cum punctis D, B" vel cum punctis oppositis coincidat, vel parum ab ipsis 
distet: casum enim eum, ubi B cum B" coincidit, vel perparum ab eo distat, 
iam supra art. 138 a disquisitione nostra exclusimus.
	        

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Gauß, Carl Friedrich. [Theoretischer Astronomischer Nachlass]. In Commission bei B. G. Teubner, 1906.
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