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Table IV from Bernoulli's article in
Acta Eruditorium 1697

Brachistochrone Part III
 A reproduction and explanation of the original curves.


  The  Brachistochrone

Bernoulli Table IV

Legend for the Figures
Fig.  I, II, III.
Solution and explanation from "JOH. BERNOULLI", i.e., (Johann, John, or Jean).
     I. "Cycloidem"     II. "Brachystochrona"     III. "Quœritur in plano verticali  - Curve Synchrona PB."
Galileo is also discussed.
Fig. IV, V, VI, VII, VIII.
Solution and explanation from "JAC. BERNOULLI", i.e., (Jacques, James or Jacob).
The "isochronam illam Hugenianm" is injected on Fig. VI.     Fig. VII. discusses "Funiculariam" while Fig. VIII. mentions "Tschirnbausium" and "Problematis Physico-Mathematici" (Tschirnhausen Cubic).
Fig. IX, X.
Solution and explanation from "HOSPITALLII",  (l'Hôpital, or L'Hospital).
Fig. XI.
"Des-Cartes curvarum" with a brief explanation under the heading of "Universalia Theoremata Eruendi".
Anonymous solution entitled, "Excerpta EX TRANSACTIONIBUS PHILOS. ANGLIC" (Recognized by Johann Bernoulli as the work of Sir Isaac Newton with the famous quote, "The lion is know by its claw."
All readers of this material will join the National Curve Bank - A MATH Archive in thanking the Huntington Library, San Marino, CA, for permitting us to enjoy this publication dating to 1697.  Interestingly, the Huntington copy was remaindered from the University of Stockholm, Sweden.

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Brachistochrone Part  II

Brachistochrone Part IV