Such are the Lines AP, AP, &c. (Tab. Conics, Fig. 20.)
They are called Abscisses of the Latin Absindo, I cut off ; as being Parts cut off from the Axis. Others call 'em Sagittæ, Arrows. See SAGITTA.
AGEOMETRESIA, a term derived from Greek, occasionally used by English writers, refers to a deficiency in understanding geometry. Kepler, for instance, was said to exhibit ageometresia when he did not provide direct geometrical methods to find certain aspects in his elliptic theory.
ALCANTARA.— Order of Alcantara, was an ancient Military Order, denominated from a City of that Name in the Kingdom of Spain. See KNIGHT, ORDER, &c.Alphonso IX. having recovered Alcantara from the Moors, in the Year 1212; committed the Custody and Defence thereof, first, to the Knights of Calatrava; and, two Years afterwards, to the Knights of the Pear-Tree, another Military Order, instituted in 1170, by Gomez Fernandez, and approved by Pope Alexander III under the Rule of St. Benedict: upon which they changed their Name, and took the Denomination of Knights of Alcantara.After the Expulsion of the Moors, and the Taking of Granada; the Sovereignty of the Order of Alcantara, and that of Calatrava, were settled in the Crown of Castile, by Ferdinand and Isabella. See CALATRAVA.In 1540, the Knights of Alcantara sued for leave to marry; which was granted them.
ALTERNATE Angles, in Geometry, are the internal Angles made by a Line cutting two Parallels, and lying on the opposite Sides of the cutting Line; the one below the first Parallel, and the other above the second. See ANGLE. Thus, a and b, and x and y, (Tab. Geometry, Fig. 46.) are Alternate Angles. There are also two external Angles, alternately opposite to the internal ones. See OPPOSITE. Alligation
ALTITUDE, Altitudo, in Geometry, the third Dimension of a Body; called also Height, or Depth. See HEIGHT; see also BODY, DIMENSION, etc.Altitude, in Optics, is usually considered as the Angle subtended between a Line drawn through the Eye, parallel to the Horizon, and a Visual Ray emitted from an Object to the Eye.For the Laws of the Vision of Altitude, see Vision.If through the two Extremes of an Object, S and T, (Tab. Optics, Fig. 13.) two Parallels, TV and SQ, be drawn; the Angle TVS, intercepted between a Ray passing through the Vertex S, and terminating the Shadow thereof in V, makes, with the right Line TV, what is called, by some Writers, the Altitude of the Luminary. Altitude, in Cosmography, is the perpendicular Height of a Body, or Object; or its Distance from the Horizon, upwards. See HEIGHT; see also HORIZON. Altitudes are divided into accessible and inaccessible. See ACCESSIBLE, and INACCESSIBLE. There are three Ways of Measuring Altitudes, viz. Geometrically, Trigonometrically, and Optically —The first is somewhat indirect and unartful; the second, performed by means of Instruments for the Purpose; and the third by Shadows. The Instruments chiefly used in measuring of Altitudes, are the Quadrant, Theodolite, Geometrical Quadrat, or Line of Shadows, &c. the Descriptions, Applications, &c. whereof, see under their respective Articles, QUADRANT, Theodolite, Quadrat.
AMBIT, of a Figure, in Geometry, is the Perimeter, Circumference, or Sum of all the bounding or encompassing Lines, that constitute or include it. See PERIMETER, CIRCUMFERENCE, etc.
ANGLE, Ἀγκύλος, in Geometry, the Aperture or mutual Inclination of two Lines, which meet, and form an Angle in their Point of Intersection. See LINE. Such is the Angle ABC, (Tab. Geometry, Fig. 91.) formed by the Lines AB, and AC, meeting in the Point A—The Lines AB and AC, are called the Legs of the Angle; and the Point of Intersection, the Vertex. See LEG and VERTEX. Angles are sometimes denoted by a single Letter affixed to the Vertex, or angular Point, as A; and sometimes by three Letters, that of the Vertex being in the middle, as BAC. The Measure of an Angle, whereby its Quantity is expressed, is an Arc, DE, described from its Vertex A, with any Radius at pleasure, between its Legs, AC and BC. See ARC. Hence Angles are distinguished by the Ratio of the Arches which they thus subtend, to the Circumference of the whole Circle. See CIRCLE and CIRCUMFERENCE.—And thus, an Angle is said to be of so many Degrees, as are the Degrees of the Arch DE, See DEGREE. Hence also, since similar Arches, AB and DE, fig. 87. have the same Ratio to their respective Circumferences; and the Circumferences contain each the same Number of Degrees; the Arches AB, and DE, which are the Measures of the two Angles ACB, and ADE, are equal; and therefore the Angles themselves are so too. Hence, again, as the Quantity of an Angle is estimated by the Ratio of the Arch, subtended by it, to the Periphery; it does not matter what Radius that Arch is described withal: But the Measures of equal Angles are always either equal Arches or similar ones; and contrarily. It follows, therefore, that the Quantity of the Angle remains still the same, though the Legs be either produced or diminished. And thus similar Angles, and in similar Figures, the Homologous or Corresponding Angles are also equal. See SIMILAR, FIGURE, &c.
ARK, or Arc, or Arch, Arēs, in Geometry, Astronomy, etc. See ARC.
Ark, Arca, in the Scripture-Language, a kind of floating Vessel built by Noah, for the Preservation of the several Species of Animals, from the Deluge. See DELUGE.
The Ark has afforded several Points of curious Enquiry among the Critics and Naturalists, relating to its Form, Capacity, Materials, Time of Building, etc. Noah is computed to have been an hundred Years in building the Ark, viz. from the Year of the World 1557, to the Flood, which happened in the Year 1656: At least, this is the common Opinion of the Learned. Origen, lib. iv. Contra Celsum; Augustine, de Civitate Dei, lib. xv. c. 27. and Contra Faustinum, lib. xii. c. 18. And in his Questions on Genesis v. and xxiii. Rupertus, lib. iv. in Genesis xx. assert as much; and are followed by Salian, Toruniel, and Spondanus:—Pelletier of Rouen declares himself of the same Opinion, in an express Dissertation, De Arca Noe, printed in 1700.
Ark, Arca, in the Scripture-Language, a kind of floating Vessel built by Noah, for the Preservation of the several Species of Animals, from the Deluge. See DELUGE.
The Ark has afforded several Points of curious Enquiry among the Critics and Naturalists, relating to its Form, Capacity, Materials, Time of Building, etc. Noah is computed to have been an hundred Years in building the Ark, viz. from the Year of the World 1557, to the Flood, which happened in the Year 1656: At least, this is the common Opinion of the Learned. Origen, lib. iv. Contra Celsum; Augustine, de Civitate Dei, lib. xv. c. 27. and Contra Faustinum, lib. xii. c. 18. And in his Questions on Genesis v. and xxiii. Rupertus, lib. iv. in Genesis xx. assert as much; and are followed by Salian, Toruniel, and Spondanus:—Pelletier of Rouen declares himself of the same Opinion, in an express Dissertation, De Arca Noe, printed in 1700.