Question: The logarithmic spiral was investigated by the mathematician who was a proponent of which branch of mathematics?

Context paragraphs:
Logarithmic norm: In mathematics, the logarithmic norm is a real-valued functional on operators, and is derived from either an inner product, a vector norm, or its induced operator norm.  The logarithmic norm was independently introduced by Germund Dahlquist and Sergei Lozinskiĭ in 1958, for square matrices.  It has since been extended to nonlinear operators and unbounded operators as well.  The logarithmic norm has a wide range of applications, in particular in matrix theory, differential equations and numerical analysis.  In the finite dimensional setting it is also referred to as the matrix measure or the Lozinskiĭ measure.

Jacob Bernoulli: Jacob Bernoulli (also known as James or Jacques; 6 January 1655 [O.S. 27 December 1654] – 16 August 1705) was one of the many prominent mathematicians in the Bernoulli family.  He was an early proponent of Leibnizian calculus and had sided with Leibniz during the Leibniz–Newton calculus controversy.  He is known for his numerous contributions to calculus, and along with his brother Johann, was one of the founders of the calculus of variations.  He also discovered the fundamental mathematical constant e.  However, his most important contribution was in the field of probability, where he derived the first version of the law of large numbers in his work "Ars Conjectandi".

Logarithmic spiral beaches: A logarithmic spiral beach is a type of beach which develops in the direction under which it is sheltered by a headland, in an area called the shadow zone.  It is characterized as a logarithmic spiral because if you look at it in plan view or aerially, it represents the same shape that is created from the logarithmic spiral relation.  These beaches are also commonly referred to as ‘half heart’ or ‘crenulate’ shaped bays, or ‘headland bays’.

Scroll (music): A scroll is the decoratively carved beginning of the neck of certain stringed instruments, mainly members of the violin family.  The scroll is typically carved in the shape of a volute (a rolled-up spiral) according to a canonical pattern, although some violins are adorned with carved heads, human and animal.  The quality of a scroll is one of the things used to judge the luthier's skill.  Instrument scrolls usually approximate a logarithmic spiral.  Although many references assert that the instrument scroll closely follows the golden spiral (a specific form of the logarithmic spiral) this assertion is demonstrably false.

Cotes's spiral: In physics and in the mathematics of plane curves, Cotes's spiral (also written Cotes' spiral and Cotes spiral) is a spiral that is typically written in one of three forms

James McMahon (mathematician): James McMahon (April 22, 1856 – June 1, 1922) was an Irish mathematician whose career was spent at Cornell University in Ithaca, New York.  He was a committed educator, and an early proponent of professionalization in the teaching of advanced mathematics in America.  A professor and Chairman of the Mathematics Department in Cornell University’s College of Arts & Sciences, McMahon was one of the earliest members of the American Mathematical Society (as the predecessor New York Mathematical Society) in 1891.  For seven years he served as associate editor of the "Annals of Mathematics".  He was also the American Association for the Advancement of Science’s Secretary (1897), Section A (Mathematics and Astronomy); General Secretary (1898), and Vice-President (1901).  McMahon was also featured in the publication, "American Men (and Women) of Science".

Eadem mutata resurgo: Eadem mutata resurgo (Word-for-word translation: Same having-changed I-rise) is a Latin phrase that literally translates to "Although changed, I arise the same" or "I rise again changed but the same".  The phrase was first known to be used by Jakob Bernoulli (1654-1705), a member of the famous Swiss mathematical family, and appears on his tombstone in Basel.  Bernoulli was referring to the fact, that the logarithmic spirals are self-similar, meaning that upon applying any similarity transformation to the spiral, the resulting spiral is congruent to the original untransformed one.  The logarithmic spiral continually appears in nature, such as with the curves of the Nautilus shell.

Logarithmic growth: In mathematics, logarithmic growth describes a phenomenon whose size or cost can be described as a logarithm function of some input.  e.g. "y" = "C" log ("x").  Note that any logarithm base can be used, since one can be converted to another by multiplying by a fixed constant.  Logarithmic growth is the inverse of exponential growth and is very slow.

Logarithmic spiral: A logarithmic spiral, equiangular spiral or growth spiral is a self-similar spiral curve which often appears in nature.  The logarithmic spiral was first described by Descartes and later extensively investigated by Jacob Bernoulli, who called it "Spira mirabilis", "the marvelous spiral".

Golden spiral: In geometry, a golden spiral is a logarithmic spiral whose growth factor is φ, the golden ratio.  That is, a golden spiral gets wider (or further from its origin) by a factor of φ for every quarter turn it makes.  A golden spiral with initial radius 1 has the following polar equation:

Supporting paragraphs: Logarithmic spiral Jacob Bernoulli
Answer: Leibnizian calculus