## Glossary Rectilinear

#### 2. Of a figure, angle, or area: bounded or formed by straight lines.

1654 Walter Charleton Physiologia 472

The Angle of Contingence, which truly differs from a right line, is less than any Rectilinear Angle, however acute.

Gassendi's mechanics shows the strong influence of the Galilean programme. He addresses the law of free-fall twice, first in a faulty treatment in De Motu (1642), and next in corrected fashion in De proportione qua gravia decidentia accelerantur (1646). In the earlier work, Gassendi focuses on forces compelling the falling body, which he takes to comprise the attractive force of magnetism and the propelling force of air behind the falling body. This combination of forces, he suggests, allows for the Galilean law that the distance traveled by bodies in free-fall is proportional to the time of fall squared. However, Gassendi mistakenly takes increases in velocity and in distances to be equivalent, leading him to manufacture a false need for greater velocity attained than what would be produced by the attractive forces alone. In De Proportione, he acknowledges this error, amends his calculations, and retreats to a causal account that rests on the single force of the terrestrial magnetic attraction. This is not one of Gassendi's empirical triumphs, though—in neither work does he make any specific reference to observations or experiments.

One notable success in the experimental domain is his performance of the Galilean test of dropping a stone from the mast of a moving ship, recorded in De Motu. Once dropped, Gassendi shows, the stone conserves its horizontal speed (equal to that of the ship, before being released) and its motion describes a parabola given its downward fall. This result successfully refutes one simple anti-Copernican argument, by showing that the Earth can move without superadding motion to terrestrial objects otherwise in motion (which superaddition, opponents of Copernicanism correctly maintained, would generate much havoc in the motion of terrestrial objects). This much Galileo surmised in his original thought experiment, though the performance was excellent publicity for the Galilean perspective and an opportunity for Gassendi to think through the issues at stake.

In this regard, Gassendi was able to take a step beyond Galileo's conclusions, drawing from this test a generalized principle of inertia (the Galilean version of inertia was fundamentally circular, given that bodies in motion would trace the earth's curve). Gassendi saw that the motion of the dropped stone at a sustained speed—in the absence of any contrary force or obstacle -- is an instance of inertial motion, albeit one where the motion is compositional (describing the parabola). Indeed, neither compositionality nor directionality had any impact on inertial motion, Gassendi concluded: any body set in motion in any direction continues, unless impeded, in rectilinear path.

1672 Isaac NEWTON Letters. 20 August, 1672. in Correspondence. (1959) I. 230

Let the five points be A, B, C, D, & E any three of which as A, B, & C joyn to make a rectilinear triangle ABC.

1728 H. PEMBERTON View Sir I. Newton's Philos. 137

What has here been said upon this rectilinear figure [etc.].

1840 D. LARDNER Geom. 223

If one side of a plane rectilinear angle revolve round its other side as an axis, it will produce the surface of a right circular cone.

#### 3. Forming or lying in a straight line.

1691 John DUNTON Voyage round World III. xi. 403

Time runs in a direct Line forward: It is a rectilinear Series of Moments, and allows no Digression.

1704 Isaac NEWTON Opticks I. II. 91

When I had caused the rectilinear sides..of the Spectrum of Colours made by the Prism to be distinctly defined.

#### 4. a. Characterized by straight lines. Also fig.: straightforward; strict, rigid.

1827 Henry SteuartThe planter's guide; or, A practical essay on the best method of giving immediate effect to wood, by the removal of large trees and underwood; being an attempt to place the art, and that of geneneral arboriculture, on fixed and phytological principles; interspersed with observations on general planting, and the improvement of real landscape. Originally intended for the climate of Scotland. (1828) page 410.

American edition: New York, G. Thorburn and sons, 1832

The rectilinear Gardens, and elaborate Topiary works handed down from antiquity.

1845 John Henry Parker, A Glossary of Terms Used in Grecian, Roman, Italian, and Gothic Architecture.. 4th edition London: C. Tilt, 1836. volume 1, page 192:--

The same rectilinear arrangement also pervaded many of the details.

notes on parker from: http://www.dictionaryofarthistorians.org/parkerj.htm

Capitalizing on the enthusiasm of Gothic revival in England, Glossary of Architecture was highly influential for both architectural historians and practicing architects of the movement.

1861 Good Words Aug. 433/1

The modern city ... has a trim, rectilinear ... air about it.

1920 E. Ray (Edwin Ray)Lankester (1847-1929) Secrets of Earth and Sea xviii. 202

The rectilinear angular decorative design which is known as the "Greek key pattern".

1826 British Critic Volume 2, page 376

It is not merely the vertical mullions that run in straight lines, but the horizontal transoms also... Hence we would call this the "Rectilinear style".

1852 Ecclesiologist 13, page 71.

To the Rectilinear Period he objected, that horizontal lines are just as much rectilinear as vertical ones, and therefore a Grecian temple is just as rectilinear as a Gothic cathedral.

1924 Cathedrals (Great Western Railway) (1926) 121

This "rectilinear" tracery was imitated in low relief on blank wall surfaces.

1962 Paul Frankl, Gothic Architecture, volume 4, page 153

The tracery of the windows contained ogee arches that is, the chapel combines Curvilinear and Rectilinear elements.

1995 Journal of the Society of Architectural Historians 54, page 302, column 2

Rebuilding of the church began ca.1390, ... starting with the presbytery in an advanced northern English rectilinear style.

#### c. Of a hand or machine saw: having a straight rather than a curved or circular blade. Now rare.

1843 Charles Holtzapffel (1806-1847, mechanical engineer and technical writer), Turning and Mechanical Manipulation Volume 2, page 739

Rectilinear sawing machines are for the most part derived from saws used by hand for similar purposes.

1854 Armengaud, Jacques-Eugène (1810-1891),Armengaud's Practical Draughtsman's Book of Industrial Design , page 172, column 2:

These results show that, for small pieces of wood, one circular 600. and even more. saw does as much work as four vertical rectilinear saws in the same time, and with the same motive power.

Note: According to University of Michigan's Making of America Database, the full title is:

The practical draughtsman's book of industrial design, and machinist's and engineer's drawing companion: forming a complete course of mechanical, engineering, and architectural drawing., translated by William Johnson from the French of M. Armengaud, the elder ... and MM. Armengaud, the younger, and Amouroux .... (Rewritten and arranged, with additional matter and plates, selections from and examples of the most useful and generally employed mechanism of the day.)