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operations of thinking itself. Great value was placed upon the ability to carry on a conversation or
argue in a wholly rational manner with the thoughts carefully linked together.
Rhetoric: Rhetoric is defined as the art of using language in such a way as to make the desired
impression upon the hearer or reader. Generally speaking, rhetoric covered the whole subject of
composition, both oral and written. In rhetoric we see the interplay of both grammar and logic.
Arithmetic: Arithmetic was originally the science or theory of numbers. Someone has said that
the teaching of arithmetic during medieval times consisted of simple calculations and complex
superstitions. This seems too simple a view, although perhaps not a wholly unreasonable one. It
seems likely that the arithmetic of the quadrivium probably consisted of four elements. These
would have been numeration, the naming of numbers; notation, the writing and reading of
numbers; counting, the act of numbering; and computation, the manipulation of numbers. For all
this simplicity, years later the mathematician Karl Gauss was able to refer to arithmetic as the
“queen of mathematics.”
Geometry: In this day of calculators and computers, mathematics holds little of mystery or
romance for any except the most dedicated mathematician. As a result it is difficult for one to
relate to Plato’s statement “geometry will draw the soul towards truth, and create the spirit of
philosophy.” To understand this, one must remember that the Greeks pursued all mathematics out
of intellectual curiosity and a zest for pure thought. They were concerned with teaching men to
reason abstractly and preparing them to contemplate the ideal and the beautiful. Their complete
absorption with geometry led them to convert mathematical ideas into geometrical ones. Their
preference for idealizations and abstractions expressed itself in a mathematical spirit whose
ultimate end was philosophy. It is essentially this Greek idealization of geometry that has carried
over into Masonry.
Astronomy: Astronomy today is one of the exact sciences and it has long since divested itself of
the metaphysics and mysticism which once characterized its studies. In the minds of all peoples,
astronomy is the science of the heavens and has been closely connected with religious tradition. It
was long thought that in the heavens would be found the supernatural causes of observed
phenomena as well as the answers to the future. Masonry has idealized astronomy as it has
geometry. The monitorial lecture tells us that, “Astronomy is that divine art, by which we are
taught to read the wisdom, strength, and beauty of the Almighty Creator in those sacred pages, the
celestial hemisphere.” For Masonry, the value of astronomy is metaphysical rather than physical
as indicated by the final sentence of the lecture. “While we are employed in the study of this
science, we must perceive unparalleled instances of wisdom and goodness, and through the whole
creation, trace the glorious Author by His works.”
Music: Somewhere back in time, man discovered that the sounds from his stringed instrument
depended upon their lengths. He further found that putting multiple strings together allowed him
to produce a pleasing harmony. His inquiring mind led him to discover that the ratio of the lengths
of the strings were simple whole numbers. So from the time of Pythagoras the study of music was
regarded as mathematical in nature. It seems strange to think of music as mathematical until one
considers the words of the philosopher and mathematician Gottfried Liebniz, “Music is the
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