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Differential Geometry and Its Applications Vol. 4 No. 3

[MATHEMATIC - GEOMETRY] FRANCESCO FELICIANO,Biblio.com

Scala Grimaldelli libro di aritmetica e geometria speculatiua e pratticale. Venezia Hertz 1669

1669113Renowned italian treatise on mathematic and Practical geometrythe use of the "Squadro Geometrico" Set Square the multiplication "per crocetta" and the first mention of the surveyor's cross Feliciano Francesco. Scala Grimaldelli libro di aritmetica e geometria speculatiua e pratticale di M. Francesco Feliciano Veronese. Diuiso in tre libri. Nel primo si tratta di cose pertinenti a Mercatanti . Nel secondo si tratta dell'arte maggiore di algebra .accresciuto in quest'vltima impressione di dottissimi problemi . Nel terzo & vltimo si dimostra il misurar della Terra . i nuovo ristampato e da molti errori corretto e accresciuto di molte cose da M. Filippo Macario Veronese . Venetia : presso Gio. Giacomo Hertz 1669.4to 188 x 120 mm contemporary paper board handwrtten titles at front board in sepia ink pp. 8 240 printer device with Galleon at title page xylographic head-letters head-pieces and end-pieces. Last printed edition of this milestone in the history of mathematic The Scala Grmaldelli is a work of outstanding importance in the history of mathematics and more than any other work influenced the teaching of this science in the sixteenth century.The book deals with commercial arithmetic treatment of roots the rule of false position algebra and a section on practical geometry. At leaf d2 recto Feliciano illustrates the method of multiplication "Per Crocetta" one of several methods that were in use in the Italian Renaissance.It is noteworthy in the part dealing with practical geometry the constant use of the "Squadro Geometrico" geometric square which appears to have been practiced in Italy since the XV century.The Scala Grimaldelli when first published was the first book describing the use of the Surveyor's Cross a simple instrument made of two bars forming a right-angled cross with sights at each end and used in setting out right angles in surveying an innovative tool at a time when long distances were often merely estimated by sight.The book was so important in the teaching of elementary mathematics that he was reprintd in numerous editions including this last one in 1669 143 years after the original edition."Few books had greater influence on the subsequent teaching of elementary mathematics" Smith. The symbology expressed in the title is fascinating: just as you need a ladder to attack a fortress and a lockpick to open a lock in the same way to approach complex mathematics you need this book.Francesco Feliciano was a mathematician of Lazesio Veronese who lived in the second half of the century. XV and in the first quarter of the XVI. He published in 1517 Libro di abbaco printed in several editions but he is best known for the book of arithmetic and speculative and practical geometry described here: Scala Grimaldelli 1526 whose subsequent editions reached the end of the XVII century. This important treatise disseminated outside Italy the ideas the notions and the methods in the field of arithmetic geometry algebra and their applications that were first exposed by Leonardo Pisano and then cultivated in italian schools. Conditions: this book was meant to be heavily used so it's rare find a copy in good condition as despite few marls of use this copy in its original binding can be defined. Provenance: I. Faded handwriten ownership signature at title page II. Contemporary handwrtten annotations and calculations on margins. Reference: Honeyman IV 1288; Michel-Michel III-29; Riccardi II-22. Giacomo Hertz

BIBLIOPATHOS FINE ARTS · Italie900,00 €

[SCIENCE - GEOMETRY] LORENZO MASCHERONIBiblio.com

1797 - La geometria del compasso

179788RARE FIRST EDITION OF LORENZO MASCHERONI's TREATISE ABOUT THE USE OF THE COMPASS IN GEOMETRYUNTRIMMED AND UNCUT COPY IN ORIGINAL PAPER WRAPPERMascheroni Lorenzo. La geometria del compasso di Lorenzo Mascheroni. Pavia : presso gli eredi di Pietro Galeazzi anno V della Repubblica francese 1797.8to 223 x 130 mm original printer's wrappers; pp. 2 XVIII 264 14 leaves of folding plates woodcut decoration at title page friezes and headletters. The principle of economy in geometric constructionsFirst edition of Mascheroni's most important work with a dedication in verse to Napoleon in which he proves that any geometrical construction of Euclidean geometry can be carried out by means of compasses alone admitting that a straight line is constructed once two of its points have been defined thus demonstrating how a certain principle of economics in geometric constructions proclaimed by all the great mathematicians of the past from Pappus to Descartes was regularly and violated by the use of two tools where only one was enough.His approach was to first demonstrate how to use the compass alone to bisect a given arc of a circle add and subtract two given segments find the fourth proportional given three segments find the point of intersection of two given lines and the points of intersection between a given line and a circle.At this point Mascheroni theoretically demonstrated how all constructions completed with ruler and compass can be considered as a composition of the elementary operations defined above and therefore obtained using only the compass. In the spirit of the Enlightenment this work is not meant to be just theoretical but is also designed to facilitate the construction of precision instruments. Although some authors such as the Danish G. Mohr had sought before Mascheroni the solution of certain geometrical problems by using the compass alone he was able to deal with the subject of the geometry of the compass with such depth and in such a general way to make his forerunner forgotten.Lorenzo Mascheroni 1750 - 1800 was an Italian mathematician scholar and academic who since 1778 taught physics and mathematics at the Bergamo seminary.His most important contributions concern mathematical analysis with studies related to integral calculus and natural logarithms construction science with its original studies on arc-breaking calculus and geometry with the demonstration that solvable problems with row and compasses can also be solved with just the compass.His name is also linked to the Euler-Mascheroni constant of which he calculated the first 32 decimal digits. The Euler – Mascheroni constant also called Euler's constant is a mathematical constant recurring in analysis and number theory usually denoted by the lowercase Greek letter gamma γ.It is defined as the limiting difference between the harmonic series and the natural logarithm.Napoleon whose passion for science and mathematics is known met Mascheroni in 1796 during the invasion northern Italy and was intrigued by his theories ion the use of the compasses becoming they say a great expert. "General we could expect from you everything but geometry lessons": with this sentence the mathematician Laplace and Lagrange welcomed Napoleon's explanations on Mascheroni's constructions whose book just a year after the Italian edition in 1798 was translated into French by Charette.Conditions: Light marks of use along the text small warmholes never touching the text in general very good copy printed on strong paper untrimmed and uncut in its original paper wrapper.References: RICCARDI P. "Biblioteca Matematica Italiana Milano 1952 vol. 1 134 9.1 "Pregiata e Rara". Pietro Galeazzi paperback

BIBLIOPATHOS FINE ARTS · Italie1 000,00 €