scholarly journals Mean and True Positions of Planets as Described in Gaṇitagannaḍi

2021 ◽  
Vol 9 ◽  
pp. 232-272
Author(s):  
B S Shylaja ◽  
Seetharam Javagal
Keyword(s):  
Seventeenth Century ◽  
Mathematical Work ◽  
Kannada Language ◽  
The Mean ◽  
Palm Leaf

The unpublished seventeenth-century Kannaḍa-language mathematical work Gaṇitagannaḍi is transmitted in a single palm-leaf manuscript.  It was composed by Śaṅkaranārāyaṇa Jōisaru of Śṛṅgeri and is a karaṇa text cast as a commentary on the Vārṣikatantrasaṅgraha by Viddaṇācārya. Gaṇitagannaḍi's unique procedures for calculations wer introduced in an earlier paper in volume 8 (2020) of this journal.  In the present paper the procedures for calculations of the mean and true positions of planets are described.

Practices of reasoning: persuasion and refutation in a seventeenth-century Chinese mathematical treatise of “linear algebra”

2020 ◽  
Vol 33 (1) ◽  
pp. 65-93
Author(s):  
Jiang-Ping Jeff Chen
Keyword(s):  
Seventeenth Century ◽  
Linear Algebra ◽  
Mathematical Work ◽  
Traditional Practices ◽  
Systematic Treatment ◽  
Mathematical Content ◽  
Mathematical Treatise ◽  
Traditional Approaches

ArgumentThis article documents the reasoning in a mathematical work by Mei Wending, one of the most prolific mathematicians in seventeenth-century China. Based on an analysis of the mathematical content, we present Mei’s systematic treatment of this particular genre of problems, fangcheng, and his efforts to refute the traditional practices in works that appeared earlier. His arguments were supported by the epistemological values he utilized to establish his system and refute the flaws in the traditional approaches. Moreover, in the context of the competition between the Chinese and Western approaches to mathematics, Mei was motivated to demonstrate that the genre of fangcheng problems was purely a “Chinese” achievement, not discussed by the Jesuits. Mei’s motivations were mostly expressed primarily in the prefaces to his works, in his correspondence with other scholars, in synopses of his poems, and in biographical records of some of his contemporaries.

scholarly journals Individuality in syntactic variation: An investigation of the seventeenth-century gerund alternation

2020 ◽  
Vol 31 (2) ◽  
pp. 279-308
Author(s):  
Lauren Fonteyn ◽  
Andrea Nini
Keyword(s):  
Seventeenth Century ◽  
Structural Variation ◽  
Population Level ◽  
Conditional Inference ◽  
Internal Factors ◽  
Syntactic Variation ◽  
Conditional Inference Tree ◽  
High Fraction ◽  
The Mean ◽  
Inference Tree

AbstractThis study investigates the extent to which there is individuality in how structural variation is conditioned over time. Earlier research already classified the diachronically unstable gerund variation as involving a high fraction of mixed-usage speakers throughout the change, whereby the proportion of the conservative variant versus the progressive variant as observable in the linguistic output of individual language users superficially resembles the mean proportion as observable at the population level. However, this study sets out to show that there can still be heterogeneity within such a centralized population in terms of how each individual conditions the observed variation. A random forest and conditional inference tree analysis of over 14,000 gerunds uttered by nineteen seventeenth-century authors is presented to show that, while the most important language-internal factors conditioning the gerund variation are adopted by (and shared between) all authors, we can still attest inter-individual variation (i) at lower levels of variable importance, and (ii) in the breadth of the range of contexts individual authors employ to condition the attested variation.

Wren the mathematician

1960 ◽  
Vol 15 (1) ◽  
pp. 107-111 ◽  
Keyword(s):  
Seventeenth Century ◽  
Present State ◽  
Mathematical Achievement ◽  
Mathematical Work ◽  
Christiaan Huygens ◽  
John Wallis ◽  
Century Thought

Today Wren’s fame rests solidly on his architectural achievement, and deservedly so. Yet in his own time, and especially before his thoughts had turned towards architecture, he was acclaimed equally for his mathematical brilliance. In a famous passage of the Principia, Newton, master mathematician himself but no flatterer, paid Wren the compliment of ranking him with John Wallis and Christiaan Huygens as a leading geometer of his day, while his supreme mathematical achievement, the rectification of the general cycloid arc, made his name known throughout Europe, earning even Pascal’s approval. It is unfortunately difficult for us to begin to justify this reputation. Wren’s mathematical work now exists, if at all, in detached fragments rescued from oblivion, some in print, and a little more in bare outline in the published work of contemporaries, especially Wallis. Collecting these scattered remains is but a necessary preliminary to any evaluation. Doubts of authorship, uncertainty as to how far existing fragments are typical of his mathematical output and the problem of assessing their importance in the context of seventeenth-century thought, all introduce their further difficulties, and in the present state of knowledge no more than a reasoned reconstruction is possible.

scholarly journals Edward Charles Titchmarsh, 1899-1963

1964 ◽  
Vol 10 ◽  
pp. 305-324
Keyword(s):  
Seventeenth Century ◽  
Royal Society ◽  
Family Background ◽  
Religious Tradition ◽  
Early Years ◽  
Mathematical Work ◽  
The Family

Edward Charles Titchmarsh was born on 1 June 1899, at Newbury; he was the son of Edward Harper and Caroline Titchmarsh, and he had an elder sister, and a younger sister and brother. His father was a Congregationalist minister and an M.A. of London University; his father’s people were tradesmen at Royston, never more than fairly prosperous, and on both sides of the family there was a strict religious tradition. Titchmarsh himself wrote an eminently readable account of his family background for his own family; it begins with the derivation of the name from the place Ticcea’s marsh and contains a record going back to the eighteenth and even seventeenth century, and ending with his own schooldays. It is written with the clarity which was characteristic of his mathematical work, and recounts his school days and the somewhat restricted background of his early years with a critical and often humorous detachment. I have used this and the notes which he made for the Royal Society in what follows, in addition to other material supplied by Mrs Titchmarsh and many mathematical friends, especially A. E. Ingham, J. L. B. Cooper and J. B. McLeod. His father was chosen later as minister of Nether Chapel in Sheffield (partly because he was a non-smoker as well as, of course, a teetotaler), and so Titchmarsh was educated at King Edward VII School, Sheffield, from 1908-1917. He wrote that they had far too much homework, and that in the upper part of the school he went on to the classical side, giving up science, and learned ‘enough Latin to pass Higher Certificate and enough Greek to fail.’ After that he specialized in mathematics, and did some physics, but experiments always baffled him and he maintained that he knew no chemistry.

Continuous Time and Instantaneous Speed in the Works of William Heytesbury and Richard Swineshead

2020 ◽  
Vol 25 (3) ◽  
pp. 205-223
Author(s):  
Robert Podkoński
Keyword(s):  
Seventeenth Century ◽  
Fourteenth Century ◽  
Continuous Time ◽  
The Mean ◽  
Instantaneous Speed ◽  
The One ◽  
Natural Philosophers

Abstract The term ‘instantaneous speed’ that appears explicitly in the works of famous Oxford fourteenth-century natural philosophers, William Heytesbury and Richard Swineshead (nicknamed The Calculator), seems odd in the context of the then accepted Aristotelian worldview for at least two reasons. First, Aristotle himself stated unambiguously that no motion can occur in an instant. Second, after fourteenth-century atomism was rejected, the majority of thinkers denied the existence of instants, understood as indivisibles. Nevertheless, both Oxford philosophers describe instantaneous speed, also in the context of the mean-speed theorem, in a way that allowed them to preserve the continuity of time. This description may seem similar to the one formulated by Newtonians in the seventeenth century, but is so only superficially, however, as their backgrounds and contexts were different.

scholarly journals Gaṇitagannaḍi - A Text of 1604 CE on Siddhāntic Astronomy in Kannaḍa

2020 ◽  
Vol 8 ◽  
pp. 13-35
Author(s):  
B. S. Shylaja ◽  
Seetharam Javagal
Keyword(s):  
Method Of Calculation ◽  
Private Collection ◽  
Unique Method ◽  
Kannada Language ◽  
Palm Leaf

From a private collection of palm leaf manuscripts the text Gaṇithagannaḍi has been unearthed and studied. The contents follow the traditional texts with all the chapters starting from the calculation of ahargaṇas to the predictions of eclipses. The text presents a unique method of calculation which the author, Viddaṇācārya, declares to be his own invention. In this paper, the procedures are described with the help of the elaborate commentary, written in Kannaḍa language, by Shankaranārāyaṇa Jōisaru of Sringeri.   This paper highlights the uniqueness of the procedure for calculating the ahargaṇa and the dhruvās for the positions of planets.  

Validation of 12-item general health questionnaire into Kannada language

2007 ◽  
Vol 25 (18_suppl) ◽  
pp. 17077-17077
Author(s):  
D. C. Javaregowda ◽  
B. Parthasarathy ◽  
A. Suresh ◽  
D. Lokanath ◽  
K. Govind Babu ◽  
...  
Keyword(s):  
Principal Component Analysis ◽  
Factor Structure ◽  
General Health ◽  
General Health Questionnaire ◽  
Principal Component ◽  
Component Analysis ◽  
Health Questionnaire ◽  
Alpha Coefficient ◽  
Kannada Language ◽  
The Mean

17077 Background: The cancer load in India is enormous and majority of the cases present in an advanced stage. There is no valid translation of 12-item General Health Questionnaire (GHQ-12) in Kannada, which is a simple but indispensable tool in the comprehensive cancer care (both for metastatic and in adjuvant settings). Therefore we thought of developing and validating the GHQ-12 Questionnaire into Kannada language. Methods: The study was conducted at kidwai memorial institute of Oncology, Bangalore, a tertiary cancer center with an annual attendance of 16,000 new cases. We have chosen educated patients who can speak and write both English and Kannada. We used ’forward-backward’ translation procedure into Kannada. We used scores from 0–3 for the Questionnaire. Total score for both languages was calculated. Internal consistency was assessed by Cronbach's alpha coefficient. Validity was performed using convergent validity. Finally, the factor structure of the questionnaire was extracted by performing principal component analysis using oblique factor solution. Results: A total of 118 patients with various malignancies were entered into the study. The mean age was 36.8 ± 12.1 years. The mean GHQ score was 21.6 ± 9.1 for the English and 22.6 ± 8.1 for Kannada. Reliability analysis showed satisfactory result (Cronbach's alpha coefficient = 0.79). The principal component analysis with oblique rotation solution showed that the GHQ-12 was a measure of psychological morbidity with four -factor structure that jointly accounted for 48 % of the variance. Conclusions: The Kannada version of the GHQ-12 is a reliable and valid instrument with a good structural characteristic. It can be used for measuring psychological well being at our institute for those patients who can read and write only Kannada. No significant financial relationships to disclose.

Photo-electric Hβ and uvby photometry

1966 ◽  
Vol 24 ◽  
pp. 170-180
Author(s):  
D. L. Crawford
Keyword(s):  
Narrow Band ◽  
Line Strength ◽  
Interference Filter ◽  
B Stars ◽  
Relative Line ◽  
The Mean ◽  
F Stars ◽  
Two Parameters ◽  
Filter Photometry ◽  
The Continuum

Early in the 1950's Strömgren (1, 2, 3, 4, 5) introduced medium to narrow-band interference filter photometry at the McDonald Observatory. He used six interference filters to obtain two parameters of astrophysical interest. These parameters he calledlandc, for line and continuum hydrogen absorption. The first measured empirically the absorption line strength of Hβby means of a filter of half width 35Å centered on Hβand compared to the mean of two filters situated in the continuum near Hβ. The second index measured empirically the Balmer discontinuity by means of a filter situated below the Balmer discontinuity and two above it. He showed that these two indices could accurately predict the spectral type and luminosity of both B stars and A and F stars. He later derived (6) an indexmfrom the same filters. This index was a measure of the relative line blanketing near 4100Å compared to two filters above 4500Å. These three indices confirmed earlier work by many people, including Lindblad and Becker. References to this earlier work and to the systems discussed today can be found in Strömgren's article inBasic Astronomical Data(7).

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

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