Literary notes about Linear (AI summary)
The word "linear" has been employed in literature with diverse meanings depending on context. In mathematical and scientific texts, it often denotes relationships or functions that exhibit constant rates of change or follow a straight-line form—for example, in discussions of differential equations, integration, and dilatation where equations or functions are described as linear [1, 2, 3, 4, 5, 6, 7, 8, 9]. In contrast, botanical texts use "linear" as a descriptive term to characterize the shape and form of plant parts, such as leaves, petals, and pods that are long and narrow in appearance [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32]. Moreover, the term extends to measurements and artistic representations, as seen when it refers to units of measure and even certain styles of drawing [33, 34, 35]. This range of applications highlights the word's versatility, serving both as a precise mathematical descriptor and as a visual and morphological qualifier in natural science.
- If the equation is linear, the general integral may be deduced from it by the variation of constants.
— from The Declaration of Independence of the United States of America by Thomas Jefferson - Integration of the linear equation of the first order dy dx + P y = Q, where P and Q denote functions of x . Examples.
— from The Declaration of Independence of the United States of America by Thomas Jefferson - Application to linear equations with constant co-efficients.
— from The Declaration of Independence of the United States of America by Thomas Jefferson - Definition of the co-efficients of linear, superficial, and cubic dilatation.
— from The Declaration of Independence of the United States of America by Thomas Jefferson - On Linear Equations.
— from The Declaration of Independence of the United States of America by Thomas Jefferson - Tangents and normals to plane curves, whose equation in linear or polar coordinates is given.
— from The Declaration of Independence of the United States of America by Thomas Jefferson - Integration of a system of two simultaneous linear equations of the first order.
— from The Declaration of Independence of the United States of America by Thomas Jefferson - 92 Case where these variables are linear functions of the independent variables.
— from The Declaration of Independence of the United States of America by Thomas Jefferson - Linear dilatation of solid bodies.
— from The Declaration of Independence of the United States of America by Thomas Jefferson - Pod compressed, linear, smooth, 5′ long, containing many compressed, heart-shaped seeds, separated by thin partitions. Habitat.
— from The Medicinal Plants of the Philippines by T. H. Pardo de Tavera - Leaves stellate, long, narrow, linear, 4-grooved.
— from The Medicinal Plants of the Philippines by T. H. Pardo de Tavera - Corolla the same size as the calyx, 5 linear petals, the lower shorter and curved.
— from The Medicinal Plants of the Philippines by T. H. Pardo de Tavera - Corolla, 5 linear, lanceolate petals, curved and imbricated.
— from The Medicinal Plants of the Philippines by T. H. Pardo de Tavera - Leaflets 12 pairs, ovate, linear, acute, soft and downy.
— from The Medicinal Plants of the Philippines by T. H. Pardo de Tavera - Calyx, 5 sepals, almost linear.
— from The Medicinal Plants of the Philippines by T. H. Pardo de Tavera - Pod 1–2° long, linear, 4-sided, containing many oval seeds, separated by filamentous partitions.
— from The Medicinal Plants of the Philippines by T. H. Pardo de Tavera - Flowers pink, verticillate, in opposite clusters around the stem, with several linear and hairy involucres at the base of each cluster.
— from The Medicinal Plants of the Philippines by T. H. Pardo de Tavera - The leaflets nearly linear with a small point at the apex, 11–13 pairs, 2 stipules to each pair.
— from The Medicinal Plants of the Philippines by T. H. Pardo de Tavera - Corolla purplish, very long, 4 straight, linear petals.
— from The Medicinal Plants of the Philippines by T. H. Pardo de Tavera - Leaflets linear, entire, glabrous, tipped with a small point.
— from The Medicinal Plants of the Philippines by T. H. Pardo de Tavera - Corolla much longer than the calyx, 5 greenish petals, linear and curved downwards.
— from The Medicinal Plants of the Philippines by T. H. Pardo de Tavera - Involucre conical, of many linear scales, enclosing 15 or more hermaphrodite disk-flowers and several pistillate ray-flowers.
— from The Medicinal Plants of the Philippines by T. H. Pardo de Tavera - Leaves opposite, linear, green, lanceolate, stipulate.
— from The Medicinal Plants of the Philippines by T. H. Pardo de Tavera - Corolla, 5 thick petals, linear, much longer than the calyx.
— from The Medicinal Plants of the Philippines by T. H. Pardo de Tavera - Corolla, 5 linear, lanceolate petals united at the base.
— from The Medicinal Plants of the Philippines by T. H. Pardo de Tavera - Leaflets 12 or more pairs, linear, with a notch at the apex, entire, glabrous.
— from The Medicinal Plants of the Philippines by T. H. Pardo de Tavera - One or more pairs of leaflets, very small, linear.
— from The Medicinal Plants of the Philippines by T. H. Pardo de Tavera - The C. sophera , L., is characterized by 10 stamens, all fertile and a smooth, linear, bivalved pod full of seeds separated by false partitions.
— from The Medicinal Plants of the Philippines by T. H. Pardo de Tavera - Pod 1° long, with linear stalk, containing many seeds separated by filamentous isthmuses. Habitat.
— from The Medicinal Plants of the Philippines by T. H. Pardo de Tavera - Leaflets linear, notched at the apex.
— from The Medicinal Plants of the Philippines by T. H. Pardo de Tavera - Leaves sessile, linear, obtuse, margins revolute, white-hoary beneath.
— from The Medicinal Plants of the Philippines by T. H. Pardo de Tavera - Leaflets small, linear, more than 40 pairs.
— from The Medicinal Plants of the Philippines by T. H. Pardo de Tavera - A rod is a unit of linear measure equivalent to 5.5 yards and also a unit of area measure equivalent to 30.25 square yards.
— from The First Book of Adam and Eve by Rutherford Hayes Platt - Linear and imitative Drawing.
— from The Declaration of Independence of the United States of America by Thomas Jefferson - Linear Drawing.
— from The Declaration of Independence of the United States of America by Thomas Jefferson
