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Movie Title Year Distributor Notes Rev Formats Awakening of Salley 1984 VCR LezOnly DO Best of VCX Classics 2 2005 VCX 1 DO Beyond the Valley of the Ultra Milkmaids 1984 4-Play Video LezOnly Blazing Redheads 1981 TGA Video O Blue Vanities 29 1988 Blue Vanities LezOnly O Blue Vanities 315 1999 Blue Vanities DO Blue Vanities 355 2000 Blue Vanities Facial DO Blue Vanities 53 1988 Blue Vanities D Blue Vanities S-534 1993 Blue Vanities LezOnly DO Bob's Lesson 1984 California Star NonSex O Diamond Collection Film 287 1983 CDI Home Video Half the Action 1980 TVX Limited Edition Film 100 1981 AVC Limo Connection 1982 VCA Lusty Ladies 3 1983 Film Collectors
Lusty Ladies 5 1983 Film Collectors Lusty Ladies 6 1983 Film Collectors LezOnly Misty: Sweet Cherry Pie 2007 Alpha Blue Archives DRO Screw Erotic Video 1 1985 Metro LezOnly Sexboat 1980 VCX 5 DRO Suze's Centerfolds 1 1979 Caballero Home Video D Suze's Centerfolds 2 1979 Caballero Home Video Facial DO Suze's Centerfolds 2 (new) 1979 Caballero Home Video Facial 1 O Suze's Centerfolds 5 1981 Caballero Home Video Facial Suze's Centerfolds 6 1981 Caballero Home Video Facial R Taboo 2 1982 Standard Video 8 DRO Toys Not Boys 2: Slutorama 1991 Filmco Releasing LezOnly Triangle of Lust 1982 VCR Facial Trouble Down Below 1981 Fantasy Video BJOnly Udderly Fantastic 1980 TGA Video Facial O Valley Girls 1981 TGA Video



by using false position method which says to "combine the excess and deficiency as the divisor; (taking) the deficiency numerator multiplied by the excess denominator and the excess numerator times the deficiency denominator, combine them as the dividend."[18] Furthermore, The Book of Computations solves systems of two equations and two unknowns using the same false position method.[14] The Nine Chapters on the Mathematical Art The Nine Chapters on the Mathematical Art is a Chinese mathematics book, its oldest archeological date being 179 AD (traditionally dated 1000 BC), but perhaps as early as 300–200 BC.[19] Although the author(s) are unknown, they made a major contribution in the eastern world. Problems are set up with questions immediately followed by answers and procedure.[16] There are no formal mathematical proofs within the text, just a step-by-step procedure.[20] The commentary of Liu Hui provided geometrical and algebraic proofs to the problems given within the text.[2] The Nine Chapters on the Mathematical Art was one of the most influential of all Chinese mathematical books and it is composed of 246 problems.[19] It was later incorporated into The Ten Computational Canons, which became the core of mathematical education in later centuries.[16] This book includes 246 problems on surveying, agriculture, partnerships, engineering, taxation, calculation, the solution of equations, and the properties of right triangles.[16] The Nine Chapters made significant additions to solving quadratic equations in a way similar to Horner's method.[4] It also made advanced contributions to "fangcheng" or what is now known as linear algebra.[14] Chapter seven solves system of linear equations with two unknowns using the false position method, similar to The Book of Computations.[14] Chapter eight deals with solving determinate and indeterminate simultaneous linear equations using positive and negative numbers, with one problem dealing with solving four equations in five unknowns.[14] The Nine Chapters solves systems of equations using methods similar to the modern Gaussian elimination and back substitution.[14] Calculation of pi Problems in The Nine Chapters on the Mathematical Art take pi to be equal to three in calculating problems related to circles and spheres, such as spherical surface area.[19] There is no explicit formula given within the text for the calculation of pi to be three, but it is used throughout the problems of both The Nine Chapters on the Mathematical Art and the Artificer's Record, which was produced in the same time period.[15] Historians believe that this figure of pi was calculated using the 3:1 relationship between the circumference and diameter of a circle.[19] Some Han mathematicians attempted to improve this number, such as Liu Xin, who is believed to have estimated pi to be 3.154.[3] There is no explicit method or record of how he calculated this estimate.[3] Division and root extraction Basic arithmetic processes such as addition, subtraction, multiplication and division were present before the Han Dynasty.[3] The Nine Chapters on the Mathematical Art take these basic operations for granted and simply instruct the reader to perform them.[14] Han mathematicians calculated square and cubed roots in a similar manner as division, and problems on division and root extraction both occur in Chapter Four of The Nine Chapters on the Mathematical Art.[21] Calculating the squared and cubed roots of numbers is done through successive approximation, the same as division, and often uses similar terms such as dividend (shi) and divisor (fa) throughout the process.[4] This process of successive approximation was then extended to solving quadratics of the second and third order, such as {\displaystyle x^{2}+a=b}{\displaystyle x^{2}+a=b}, using a method similar to Horner's method.[4] The method was not extended to solve quadratics of the nth order during the Han Dynasty; however, this method was eventually used to solve these equations.[4] Fangcheng on a counting board Linear algebra The Book of Computations is the first known text to solve systems of equations with two unknowns.[14] There are a total of three sets of problems within The Book of Computations involving solving systems of equations with the false position method, which again are put into practical terms.[14] Chapter Seven of The Nine Chapters on the Mathematical Art also deals with solving a system of two equations with two unknowns with the false position method.[14] To solve for the greater of the two unknowns, the false position method instructs the reader to cross-multiply the minor terms or zi (which are the values given for the excess and deficit) with the major terms mu.[14] To solve for the lesser of the two unknowns, simply add the minor terms together.[14] Chapter Eight of The Nine Chapters on the Mathematical Art deals with solving infinite equations with infinite unknowns.[14] This process is referred to as the "fangcheng procedure" throughout the chapter.[14] Many historians chose to leave the term fangcheng untranslated due to conflicting evidence of what the term means. Many historians translate the word to linear algebra today. In this chapter, the process of Gaussian elimination and back-substitution are used to solve systems of equations with many unknowns.[14] Problems were done on a counting board and included the use of negative numbers as well as fractions.[14] The counting board was effectively a matrix, where the top line is the first variable of one equation and the bottom was the last.[14] Liu Hui's commentary on The Nine Chapters on the Mathematical Art Liu Hui's exhaustion method Liu Hui's commentary on The Nine Chapters on the Mathematical Art is the earliest edition of the original text available.[19] Hui is believed by most to be a mathematician shortly after the Han dynasty. Within his commentary, Hui qualified and proved some of the problems from either an algebraic or geometrical standpoint.[17] For instance, throughout The Nine Chapters on the Mathematical Art, the value of pi is taken to be equal to three in problems regarding circles or spheres.[15] In his commentary, Liu Hui finds a more accurate estimation of pi using the method of exhaustion.[15] The method involves creating successive polynomials within a circle so that eventually the area of a higher-order polygon will be identical to that of the circle.[15] From this method, Liu Hui asserted that the value of pi is about 3.14.[3] Liu Hui also presented a geometric proof of square and cubed root extraction similar to the Greek method, which involved cutting a square or cube in any line or section and determining the square root through symmetry of the remaining rectangles.[21] Mathematics in the period of disunity Liu Hui's Survey of sea island Sunzi algorithm for division 400 AD al Khwarizmi division in the 9th century Statue of Zu Chongzhi. In the third century Liu Hui wrote his commentary on the Nine Chapters and also wrote Haidao Suanjing which dealt with using Pythagorean theorem (already known by the 9 chapters), and triple, quadruple triangulation for surveying; his accomplishment in the mathematical surveying exceeded those accomplished in the west by a millennium.[22] He was the first Chinese mathematician to calculate p=3.1416 with his p algorithm. He discovered the usage of Cavalieri's principle to find an accurate formula for the volume of a cylinder, and also developed elements of the infinitesimal calculus during the 3rd century CE. fraction interpolation for pi In the fourth century, another influential mathematician named Zu Chongzhi, introduced the Da Ming Li. This calendar was specifically calculated to predict many cosmological cycles that will occur in a period of time. Very little is really known about his life. Today, the only sources are found in Book of Sui, we now know that Zu Chongzhi was one of the generations of mathematicians. He used Liu Hui's pi-algorithm applied to a 12288-gon and obtained a value of pi to 7 accurate decimal places (between 3.1415926 and 3.1415927), which would remain the most accurate approximation of p available for the next 900 years. He also applied He Chengtian's interpolation for approximating irrational number with fraction in his astronomy and mathematical works, he obtained {\displaystyle {\tfrac {355}{113}}}\tfrac{355}{113} as a good fraction approximate for pi; Yoshio Mikami commented that neither the Greeks, nor the Hindus nor Arabs knew about this fraction approximation to pi, not until the Dutch mathematician Adrian Anthoniszoom rediscovered it in 1585, "the Chinese had therefore been possessed of this the most extraordinary of all fractional values over a whole millennium earlier than Europe"[23] Along with his son, Zu Geng, Zu Chongzhi applied the Cavalieri's principle to find an accurate solution for calculating the volume of the sphere. Besides containing formulas for the volume of the sphere, his book also included formulas of cubic equations and the accurate value of pi. His work, Zhui Shu was discarded out of the syllabus of mathematics during the Song dynasty and lost. Many believed that Zhui Shu contains the formulas and methods for linear, matrix algebra, algorithm for calculating the value of p, formula for the volume of the sphere. The text should also associate with his astronomical methods of interpolation, which would contain knowledge, similar to our modern mathematics. A mathematical manual called Sunzi mathematical classic dated between 200–400 CE contained the most detailed step by step description of multiplication and division algorithm with counting rods. Intriguingly, Sunzi may have influenced the development of place-value systems and place-value systems and the associated Galley division in the West. European sources learned place-value techniques in the 13th century, from a Latin translation an early-9th-century work by Al-Khwarizmi. Khwarizmi's presentation is almost identical to the division algorithm in Sunzi, even regarding stylistic matters (for example, using blank spaces to represent trailing zeros); the similarity suggests that the results may not have been an independent discovery. Islamic commentators on Al-Khwarizmi's work believed that it primarily summarized Hindu knowledge; Al-Khwarizmi's failure to cite his sources makes it difficult to determine whether those sources had in turn learned the procedure from China.[24] In the fifth century the manual called "Zhang Qiujian suanjing" discussed linear and quadratic equations. By this point the Chinese had the concept of negative numbers. Tang mathematics By the Tang Dynasty study of mathematics was fairly standard in the great schools. The Ten Computational Canons was a collection of ten Chinese mathematical works, compiled by early Tang dynasty mathematician Li Chunfeng (??? 602–670), as the official mathematical texts for imperial examinations in mathematics. The Sui dynasty and Tang dynasty ran the "School of Computations".[25] Wang Xiaotong was a great mathematician in the beginning of the Tang Dynasty, and he wrote a book: Jigu Suanjing (Continuation of Ancient Mathematics), where numerical solutions which general cubic equations appear for the first time[26] The Tibetans obtained their first knowledge of mathematics (arithmetic) from China during the reign of Nam-ri srong btsan, who died in 630.[27][28] The table of sines by the Indian mathematician, Aryabhata, were translated into the Chinese mathematical book of the Kaiyuan Zhanjing, compiled in 718 AD during the Tang Dynasty.[29] Although the Chinese excelled in other fields of mathematics such as solid geometry, binomial theorem, and complex algebraic formulas,early forms of trigonometry were not as widely appreciated as in the contemporary Indian and Islamic mathematics.[30] Yi Xing, the mathematician and Buddhist monk was credited for calculating the tangent table. Instead, the early Chinese used an empirical substitute known as chong cha, while practical use of plane trigonometry in using the sine, the tangent, and the secant were known.[29] Yi Xing was famed for his genius, and was known to have calculated the number of possible positions on a go board game (though without a symbol for zero he had difficulties expressing the number). Song and Yuan mathematics Northern Song Dynasty mathematician Jia Xian developed an additive multiplicative method for extraction of square root and cubic root which implemented the "Horner" rule.[31] Yang Hui triangle (Pascal's triangle) using rod numerals, as depicted in a publication of Zhu Shijie in 1303 AD Four outstanding mathematicians arose during the Song Dynasty and Yuan Dynasty, particularly in the twelfth and thirteenth centuries: Yang Hui, Qin Jiushao, Li Zhi (Li Ye), and Zhu Shijie. Yang Hui, Qin Jiushao, Zhu Shijie all used the Horner-Ruffini method six hundred years earlier to solve certain types of simultaneous equations, roots, quadratic, cubic, and quartic equations. Yang Hui was also the first person in history to discover and prove "Pascal's Triangle", along with its binomial proof (although the earliest mention of the Pascal's triangle in China exists before the eleventh century AD). Li Zhi on the other hand, investigated on a form of algebraic geometry based on tian yuán shù. His book; Ceyuan haijing revolutionized the idea of inscribing a circle into triangles, by turning this geometry problem by algebra instead of the traditional method of using Pythagorean theorem. Guo Shoujing of this era also worked on spherical trigonometry for precise astronomical calculations. At this point of mathematical history, a lot of modern western mathematics were already discovered by Chinese mathematicians. Things grew quiet for a time until the thirteenth century Renaissance of Chinese math. This saw Chinese mathematicians solving equations with methods Europe would not know until the eighteenth century. The high point of this era came with Zhu Shijie's two books Suanxue qimeng and the Siyuan yujian. In one case he reportedly gave a method equivalent to Gauss's pivotal condensation. Qin Jiushao (c. 1202–1261) was the first to introduce the zero symbol into Chinese mathematics.[32] Before this innovation, blank spaces were used instead of zeros in the system of counting rods.[33] One of the most important contribution of Qin Jiushao was his method of solving high order numerical equations. Referring to Qin's solution of a 4th order equation, Yoshio Mikami put it: "Who can deny the fact of Horner's illustrious process being used in China at least nearly six long centuries earlier than in Europe?"[34] Qin also solved a 10th order equation.[35] Pascal's triangle was first illustrated in China by Yang Hui in his book Xiangjie Jiuzhang Suanfa (??????), although it was described earlier around 1100 by Jia Xian.[36] Although the Introduction to Computational Studies (????) written by Zhu Shijie (fl. 13th century) in 1299 contained nothing new in Chinese algebra, it had a great impact on the development of Japanese mathematics.[37] Algebra Ceyuan haijing Main article: Ceyuan haijing Li Ye's inscribed circle in triangle:Diagram of a round town Yang Hui's magic concentric circles – numbers on each circle and diameter (ignoring the middle 9) sum to 138 Ceyuan haijing (Chinese: ????; pinyin: Cèyuán Haijìng), or Sea-Mirror of the Circle Measurements, is a collection of 692 formula and 170 problems related to inscribed circle in a triangle, written by Li Zhi (or Li Ye) (1192–1272 AD). He used Tian yuan shu to convert intricated geometry problems into pure algebra problems. He then used fan fa, or Horner's method, to solve equations of degree as high as six, although he did not describe his method of solving equations.[38] "Li Chih (or Li Yeh, 1192–1279), a mathematician of Peking who was offered a government post by Khublai Khan in 1206, but politely found an excuse to decline it. His Ts'e-yuan hai-ching (Sea-Mirror of the Circle Measurements) includes 170 problems dealing with[...]some of the problems leading to polynomial equations of sixth degree. Although he did not describe his method of solution of equations, it appears that it was not very different from that used by Chu Shih-chieh and Horner. Others who used the Horner method were Ch'in Chiu-shao (ca. 1202 – ca.1261) and Yang Hui (fl. ca. 1261–1275). Jade Mirror of the Four Unknowns Facsimile of Zhu Shijie's Jade Mirror of Four Unknowns Si-yüan yü-jian (????), or Jade Mirror of the Four Unknowns, was written by Zhu Shijie in 1303 AD and marks the peak in the development of Chinese algebra. The four elements, called heaven, earth, man and matter, represented the four unknown quantities in his algebraic equations. It deals with simultaneous equations and with equations of degrees as high as fourteen. The author uses the method of fan fa, today called Horner's method, to solve these equations


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