The Young Mathematician's Guide: Being a Plain and Easy Introduction to the Mathematicks ... With an Appendix of Practical Gauging |
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Page 287
... TRIANGLES . There are two Kinds of Triangles , viz . Plain and Spherical ; but I shall not give any Definition of the Spherical , because they more im- mediately relate to Aftronomy . I. A PLAIN TRIANGLE is a Figure whofe Area is ...
... TRIANGLES . There are two Kinds of Triangles , viz . Plain and Spherical ; but I shall not give any Definition of the Spherical , because they more im- mediately relate to Aftronomy . I. A PLAIN TRIANGLE is a Figure whofe Area is ...
Page 288
... TRIANGLE , is that which hath all its Three Sides equal ; as the Figure ABC That is , AB = BC = AC . B A D 3. An IsosCELES TRIANGLE , is that which hath only Two of its Sides equal , as the Figure BDG : That is , BDDG ; but the Third ...
... TRIANGLE , is that which hath all its Three Sides equal ; as the Figure ABC That is , AB = BC = AC . B A D 3. An IsosCELES TRIANGLE , is that which hath only Two of its Sides equal , as the Figure BDG : That is , BDDG ; but the Third ...
Page 289
... Triangle is ufually called the Bafe ; the other two are only called Sides or Legs . 8. The Altitude or height of any Plain Triangle , is the Length of a Right Line let fall perpendicular from any of its Angles , upon the Side oppofite ...
... Triangle is ufually called the Bafe ; the other two are only called Sides or Legs . 8. The Altitude or height of any Plain Triangle , is the Length of a Right Line let fall perpendicular from any of its Angles , upon the Side oppofite ...
Page 290
... Triangles , being denoted by the prick'd Line AC in the last Figure . 8. All Right - lin'd Figures , that have more than four Sides , are call'd Polygons , whether they be regular or irregular . 9. A Regular Polygon is that which hath ...
... Triangles , being denoted by the prick'd Line AC in the last Figure . 8. All Right - lin'd Figures , that have more than four Sides , are call'd Polygons , whether they be regular or irregular . 9. A Regular Polygon is that which hath ...
Page 296
... Triangle requir❜d . A PROBLEM XI . Three Right - lines being given , to form them into a Triangle , ( provided any two of them , taken together , be longer than the Third ) ( 22. e . 1. ) Let the given Lines be Make either of the ...
... Triangle requir❜d . A PROBLEM XI . Three Right - lines being given , to form them into a Triangle , ( provided any two of them , taken together , be longer than the Third ) ( 22. e . 1. ) Let the given Lines be Make either of the ...
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Common terms and phrases
alfo Amount Angles Anſwer Arch Area Arithmetick Bafe becauſe Cafe call'd Cathetus Circle Circle's Confequently Cube Cubick Inches Cyphers Decimal defcribe Demonftration Denomination Diameter Difference divided Dividend Divifion Divifor eafily eafy eaſy Ellipfis equal Equation Example Extreams faid fame fecond feven feveral fhall fhew fingle firft firft Term firſt fome Fractions Fruftum ftand fubtract fuch Gallons Geometrical given hath Height Hence Hyperbola infinite Series Intereft juft laft Latus Rectum leffer lefs Lemma Logarithm Meaſure muft multiply muſt Number of Terms Parabola Parallelogram Periphery Perpendicular Places of Figures plain Point Pound Product Progreffion propofed Proportion Quantities Queft Queſtion Radius Reafon Refolvend reft Right Line Right-angled Right-line Root Rule Sect Segment Series Side Sine Square Suppofe Surd Tangent thefe Theorem theſe thofe thoſe Tranfverfe Triangle Troy Weight ufually Uncia uſeful Vulgar Fractions whofe whole Numbers
Popular passages
Page 467 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, &c.
Page 217 - Man playing at hazard won at the first throw as much money as he had in his pocket ; at the second throw he won 5 shillings more than the square root of what he then had ; at the third throw he won the square of all he then had ; and then he had ill 2. 16«.
Page 471 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 138 - If equal quantities be added to equal quantities, the fums will be equal. 2. If equal quantities be taken from equal quantities, the remainders will be equal. 3. If equal quantities be multiplied by equal quantities, the produits will be equal.
Page 106 - The particular Rates of all the Ingredients propofed to be mixed, the Mean Rate of the whole Mixture, and any one of the Quantities to be mixed being given: Thence to find how much of every one of the other Ingredients is requifite to compofe the Mixture.
Page 90 - If 2 men can do 12 rods of ditching in 6 days ; how many rods may be done by 8 men in 24 days ? Ans.
Page 23 - The original of all weights, used in England, was a grain or corn of wheat, gathered out of the middle of the ear ; and being well dried, 32 of them were to make one pennyweight, 20 pennyweights one ounce, and 12 ounces one pound. But, in later times, it was thought sufficient to divide the same pennyweight into 24 equal parts, still called grains, being the least weight now in common use; and from hence the rest are computed.
Page 470 - In any triangle, the sides are proportional to the sines of the opposite angles, ie. t abc sin A sin B sin C...
Page 180 - When any number of quantities are proportionals, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents.
Page 471 - FG 5 that is in Words, half the Sum of the Legs, Is to half their Difference, As the Tangent of half the Sum of the oppofite Angles, Is to the Tangent of half their Difference : But Wholes are as their Halves ; wherefore the Sum of the Legs, Is...