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Historical comments.

Early on, the study of logarithms and logarithmic tables was incorporated into trigonometry. For more on this background from the perspective of the history of trigonometry education, search through the following dissertation for the word logarithm:

Van Sickle, J. (2011). A History of Trigonometry Education in the United States: 1776-1900 (Doctoral dissertation, Columbia University). Link.

Example: You can find a book from 1914 entitled "Trigonometry with the Theory and Use of Logarithms."

Here is an excerpt:

At the least, the author seems to realize that finding the hypotenuse using the Pythagorean Theorem is more sensible; but it is strange that this would even need saying. JPBurke's informative answer mentions Eileen Donoghue, which made me wonder about the history of logarithms with regard to the New York Regents. (Donoghue is an excellent source for historical information about curricula, textbooks, and the Regents in particular; I mentioned the same 2003 article by her in an earlier MESE post.) It seems that four years after the above-mentioned book was published, a 1918 article in The Mathematics Teacher argues that logarithms should be learned in intermediate algebra, rather than "consigning" it to trigonometry.

The citation for this article is:

Decker, F. F. (1918). The New York State Regents Syllabus in Intermediate Algebra. The Mathematics Teacher, 11(1), 1-8. Jstor.

A free copy of the article can be found here, from which I quote:

The introduction to logarithms is placed in intermediate algebra. Consigning this topic to trigonometry has several disadvantages. Many students who carry their mathematical study through the course in trigonometry seem to get the idea that the usefulness of logarithms is confined to trigonometry. Those who do not reach trigonometry lose what is at once an important tool and an elegant system. In the separation of the treatment of exponents and logarithms the theory seems to contain a discontinuity. The laws for commensurable exponents are carefully proved and then the theory of logarithms is made to appear to rest on that of exponents. But most of the logarithms used are incommensurable! The plan here proposed is to introduce incommensurable exponents with reference to the continuity of an exponential curve and to pass immediately to logarithms.

The author also cites a separate document arguing that logarithms be studied along with exponents:

[A report] of the Committee on the Teaching of Mathematics to Students of Engineering, calls for the teaching of logarithms in logical connection with the subject of exponents rather than with trigonometry.

This report is foot-noted as:

"Syllabus of Mathematics," Society for the Promotion of Engineering Education, 1912.

but an APA citation is:

American Society for Engineering Education. Committee on the Teaching of Mathematics to Students of Engineering. (1912). Syllabus of mathematics: a symposium. New Era Printing Co..

The report can be found on google books; here is the relevant excerpt:

Evidently, the study of logarithms within trigonometry is widespread enough by 1912 to warrant comments from a group of engineering educators. For now, I will not pursue the connections between these two subjects any further, but I would not be surprised if the disentangling of logs from trig resulted in the former being placed later in the curriculum than you might consider ideal from a more modern perspective.

Historical comments.

Early on, the study of logarithms and logarithmic tables was incorporated into trigonometry. For more on this background from the perspective of the history of trigonometry education, search through the following dissertation for the word logarithm:

Van Sickle, J. (2011). A History of Trigonometry Education in the United States: 1776-1900 (Doctoral dissertation, Columbia University). Link.

Example: You can find a book from 1914 entitled "Trigonometry with the Theory and Use of Logarithms."

Here is an excerpt:

At the least, the author seems to realize that finding the hypotenuse using the Pythagorean Theorem is more sensible; but it is strange that this would even need saying. JPBurke's informative answer mentions Eileen Donoghue, which made me wonder about the history of logarithms with regard to the New York Regents. (Donoghue is an excellent source for historical information about curricula, textbooks, and the Regents in particular; I mentioned the same 2003 article by her in an earlier MESE post.) It seems that four years after the above-mentioned book was published, a 1918 article in The Mathematics Teacher argues that logarithms should be learned in intermediate algebra, rather than "consigning" it to trigonometry.

The citation for this article is:

Decker, F. F. (1918). The New York State Regents Syllabus in Intermediate Algebra. The Mathematics Teacher, 11(1), 1-8. Jstor.

A free copy of the article can be found here, from which I quote:

The introduction to logarithms is placed in intermediate algebra. Consigning this topic to trigonometry has several disadvantages. Many students who carry their mathematical study through the course in trigonometry seem to get the idea that the usefulness of logarithms is confined to trigonometry. Those who do not reach trigonometry lose what is at once an important tool and an elegant system. In the separation of the treatment of exponents and logarithms the theory seems to contain a discontinuity. The laws for commensurable exponents are carefully proved and then the theory of logarithms is made to appear to rest on that of exponents. But most of the logarithms used are incommensurable! The plan here proposed is to introduce incommensurable exponents with reference to the continuity of an exponential curve and to pass immediately to logarithms.

The author also cites a separate document arguing that logarithms be studied along with exponents:

[A report] of the Committee on the Teaching of Mathematics to Students of Engineering, calls for the teaching of logarithms in logical connection with the subject of exponents rather than with trigonometry.

This report is foot-noted as:

"Syllabus of Mathematics," Society for the Promotion of Engineering Education, 1912.

but an APA citation is:

American Society for Engineering Education. Committee on the Teaching of Mathematics to Students of Engineering. (1912). Syllabus of mathematics: a symposium. New Era Printing Co..

The report can be found on google books; here is the relevant excerpt:

Evidently, the study of logarithms within trigonometry is widespread enough by 1912 to warrant comments from a group of engineering educators. For now, I will not pursue the connections between these two subjects any further, but I would not be surprised if the disentangling of logs from trig resulted in the former being placed later in the curriculum than you might consider ideal from a more modern perspective.

I expect that logarithms were conceived of somewhat differently when curricula had a bigger focus on computations, and at a time when students had logarithm tables (rather than calculators). It appears that, at some point, the study of logarithms was somehow incorporated into trigonometry. This does not seem like a very sensible decision to me, but I cannot specify offhand the historical reasons for it.

Early on, the study of logarithms and logarithmic tables was incorporated into trigonometry. For more on this background from the perspective of the history of trigonometry education, search through the following dissertation for the word logarithm:

Van Sickle, J. (2011). A History of Trigonometry Education in the United States: 1776-1900 (Doctoral dissertation, Columbia University). Link.

Historical comments.

I expect that logarithms were conceived of somewhat differently when curricula had a bigger focus on computations, and at a time when students had logarithm tables (rather than calculators). It appears that, at some point, the study of logarithms was somehow incorporated into trigonometry. This does not seem like a very sensible decision to me, but I cannot specify offhand the historical reasons for it.

Example: You can find a book from 1914 entitled "Trigonometry with the Theory and Use of Logarithms."

Here is an excerpt:

At the least, the author seems to realize that finding the hypotenuse using the Pythagorean Theorem is more sensible; but it is strange that this would even need saying. JPBurke's informative answer mentions Eileen Donoghue, which made me wonder about the history of logarithms with regard to the New York Regents. (Donoghue is an excellent source for historical information about curricula, textbooks, and the Regents in particular; I mentioned the same 2003 book by her in an earlier MESE post.) It seems that four years after the above-mentioned book was published, a 1918 article in The Mathematics Teacher argues that logarithms should be learned in intermediate algebra, rather than "consigning" it to trigonometry.

The citation for this article is:

Decker, F. F. (1918). The New York State Regents Syllabus in Intermediate Algebra. The Mathematics Teacher, 11(1), 1-8. Jstor.

A free copy of the article can be found here, from which I quote:

The introduction to logarithms is placed in intermediate al gebra. Consigning this topic to trigonometry has several dis advantages. Many students who carry their mathematical study through the course in trigonometry seem to get the idea that the usefulness of logarithms is confined to trigonometry. Those who do not reach trigonometry lose what is at once an important tool and an elegant system. In the separation of the treatment of exponents and logarithms the theory seems to contain a dis continuity. The laws for commensurable exponents are care fully proved and then the theory of logarithms is made to appear to rest on that of exponents. But most of the logarithms used are incommensurable  ! The plan here proposed is to introduce incommensurable exponents with reference to the continuity of an exponential curve and to pass immediately to logarithms.

The author also cites a separate document arguing that logarithms be studied along with exponents:

[A report] of the Committee on the Teaching of Mathematics to Students of Engineering, calls for the teaching of logarithms in logical connection with the subject of exponents rather than with trigonometry.

This report is foot-noted as:

"Syllabus of Mathematics," Society for the Promotion of Engineering Education, 1912.

but an APA citation is:

American Society for Engineering Education. Committee on the Teaching of Mathematics to Students of Engineering. (1912). Syllabus of mathematics: a symposium. New Era Printing Co..

The report can be found on google books; here is the relevant excerpt:

Evidently, the study of logarithms within trigonometry is widespread enough by 1912 to warrant comments from a group of engineering educators. For now, I will not pursue the connections between these two subjects any further, but I would not be surprised if the disentangling of logs from trig resulted in the former being placed later in the curriculum than you might consider ideal from a more modern perspective.

Historical comments.

I expect that logarithms were conceived of somewhat differently when curricula had a bigger focus on computations, and at a time when students had logarithm tables (rather than calculators). It appears that, at some point, the study of logarithms was somehow incorporated into trigonometry. This does not seem like a very sensible decision to me, but I cannot specify offhand the historical reasons for it.

Example: You can find a book from 1914 entitled "Trigonometry with the Theory and Use of Logarithms."

Here is an excerpt:

At the least, the author seems to realize that finding the hypotenuse using the Pythagorean Theorem is more sensible; but it is strange that this would even need saying. JPBurke's informative answer mentions Eileen Donoghue, which made me wonder about the history of logarithms with regard to the New York Regents. (Donoghue is an excellent source for historical information about curricula, textbooks, and the Regents in particular; I mentioned the same 2003 article by her in an earlier MESE post.) It seems that four years after the above-mentioned book was published, a 1918 article in The Mathematics Teacher argues that logarithms should be learned in intermediate algebra, rather than "consigning" it to trigonometry.

The citation for this article is:

Decker, F. F. (1918). The New York State Regents Syllabus in Intermediate Algebra. The Mathematics Teacher, 11(1), 1-8. Jstor.

A free copy of the article can be found here, from which I quote:

The introduction to logarithms is placed in intermediate algebra. Consigning this topic to trigonometry has several disadvantages. Many students who carry their mathematical study through the course in trigonometry seem to get the idea that the usefulness of logarithms is confined to trigonometry. Those who do not reach trigonometry lose what is at once an important tool and an elegant system. In the separation of the treatment of exponents and logarithms the theory seems to contain a discontinuity. The laws for commensurable exponents are carefully proved and then the theory of logarithms is made to appear to rest on that of exponents. But most of the logarithms used are incommensurable! The plan here proposed is to introduce incommensurable exponents with reference to the continuity of an exponential curve and to pass immediately to logarithms.

The author also cites a separate document arguing that logarithms be studied along with exponents:

[A report] of the Committee on the Teaching of Mathematics to Students of Engineering, calls for the teaching of logarithms in logical connection with the subject of exponents rather than with trigonometry.

This report is foot-noted as:

"Syllabus of Mathematics," Society for the Promotion of Engineering Education, 1912.

but an APA citation is:

American Society for Engineering Education. Committee on the Teaching of Mathematics to Students of Engineering. (1912). Syllabus of mathematics: a symposium. New Era Printing Co..

The report can be found on google books; here is the relevant excerpt:

Evidently, the study of logarithms within trigonometry is widespread enough by 1912 to warrant comments from a group of engineering educators. For now, I will not pursue the connections between these two subjects any further, but I would not be surprised if the disentangling of logs from trig resulted in the former being placed later in the curriculum than you might consider ideal from a more modern perspective.