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" In like manner, when it is said, that " triangles on the same base, and between the same parallels, are equal... "
The Theory and Practice of Surveying: Containing All the Instructions ... - Página 173
por Robert Gibson - 1832 - 348 páginas
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The Works of Dugald Stewart: Elements of the philosophy of the human mind

Dugald Stewart - 1829
...which experience is equally incompetent to disprove or to confirm 1 In like manner, when it is said, that " triangles on the same base, and between the same parallels are equal," do we feel ourselves the less ready to give our assent to the demonstration, if it should be supposed,...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - 1829 - 186 páginas
...triangle is half of a parallelogram on the same base and between the same parallels (41. 1.), and all triangles on the same base and between the same parallels are equal (37.1.); consequently ka b will denote the number of square feet in any plane triangle. Hence the surface...
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The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

Euclides - 1833
...THEOR. Parallelograms upon equal bases and between the same pa~ rallels, are equal. PROP. 37, THEOR. Triangles on the same base, and between the same parallels, are equal. Draw through one extremity of the base (to meet the line parallel, to the base,) lines respectively...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - 390 páginas
...occurred in the preceding books. 1. Thus it was proved in the 37th proposition of the first book, that all triangles on the same base, and between the same parallels, are equal in area : and hence, if only the base and area of a triangle be given, its vertex may be at any point...
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Crocker's Elements of land surveying. To which are added, Tables of six ...

Abraham Crocker - 1841
...triangle constructed — scalenous triangle - - 34 Right angled triangle - - - - 36 Peculiar properties of triangles on the same base, and between the same parallels are equal - - 37 Similar triangles, what — their sides proportional - 37 The longest side opposite the greatest...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 352 páginas
...in the preceding books. 1. Thus, it was proved in the 37th proposition of the first book, that all triangles on the same base, and between the same parallels, are equal in area: and hence, if only the base and area of a triangle be given, its vertex may be at any point...
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The New American Practical Navigator; Being an Epitome of Navigation ...

Nathaniel Bowditch - 1846 - 451 páginas
...therefore the three parallelograms ABDC, BDFE, and EFHG, are equal to each other. Cor. Hence it follows, that triangles on the same base, and between the same parallels, are equal, since they are the half ol the parallelograms on the same base and between the same parallels (by Art....
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The Cambridge and Dublin Mathematical Journal

1848
...BOB. The former of the above propositions seems to be a proper generalization of Euclid's theorem " that triangles on the same base and between the same parallels are equal." If we have any number of surfaces of definite extent, either plane or curved, and we form pyramids...
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Introduction to lineal drawing and mensuration

Henry Pickton - 1847 - 48 páginas
...angles of a triangle are together less than two right angles. (See EUCLID, Book I. Prop, xxii.) 6. Triangles on the same base and between the same parallels are equal. (See EUCLID, Book I. Prop, xxxvii.) 7. If a parallelogram and a triangle be on the same base, the parallelogram...
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The Cambridge and Dublin Mathematical Journal, Volumen5

1850
...BOB'. The former of the above propositions seems to be a proper generalization of Euclid's theorem " that triangles on the same base and between the same parallels are equal." If we have any number of surfaces of definite extent, either plane or curved, and we form pyramids...
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