The trissotetras: or, a most exquisite table for resolving all manner of triangles, whether plaine or sphericall, rectangular or obliquangular, with greater facility, then ever hitherto hath been practised: most necessary for all such as would attaine to the exact knowledge of fortification, dyaling, navigation, surveying, architecture, the art of shadowing, taking of heights, and distances, the use of both the globes, perspective, the skill of making the maps, the theory of the planets, the calculating of their motions, and of all other astronomicall computations whatsoever. Now lately invented, and perfected, explained, commented on, and with all possible brevity, and perspicuity, in the hiddest, and most re-searched mysteries, from the very first grounds of the science it selfe, proved, and convincingly demonstrated. / By Sir Thomas Urquhart of Cromartie Knight. Published for the benefit of those that are mathematically affected.

The Diatyposis of the whole Doctrine of Triangles.

• The plane Triangles have 13. Moods.
  • Planorectangulars 7.
    • 1 Upalem.
      [illustration]
    • 2 Uberman.
      [illustration]
    • 3 Uphener.
      [illustration]
    • 4 Ekarul.
      [illustration]
    • 5 Egalem.
      [illustration]
    • 6 Echemun.
      [illustration]
    • 7 Etena••.
      [illustration]
  • Planobliquangulars. 6.
    • 1 Danarele.
      [illustration]
    • 2 There••abmo.
      [illustration]
    • 3 Zelemabne.
      [illustration]
    • 4 Xemenoro.
      [illustration]
    • 5 Shenerolem.
      [illustration]
    • 6 Pserelema.
      [illustration]
  • The Sphericals have 28 Moods.
    • Orthogonosphericals. 16.
      • 1. Upalam.
      • 2. Ubamen.
      • 3. Uphanep.
      • 4. Ukelamb.
      • 5. Ugemon.
      • 6. Uchener
      • 7. E••alum
      • 8. Edamon.
      • 9. Ethaner.
      • 10. Ezolum.
      • 11. Exoman.
      • 12. Epsoner.
      • 13. Alamun.
      • 14. Amaner.
      • 15. Enerul.
      • 16. E••elam.
      [illustration]

      Of these 16. Mood 〈◊〉〈◊〉 Moods of V••••••gen ••re prounded up∣on the Axi••••re of Supro••••••.

      The 8. of Pubkutetke¦psaler on Sbaprotea: and the 5. of Uchedezex∣am on Proso

      By these 16. Repre∣sentatives, 1. Le••. 2. Yet. 3. R••c 4. Cle. 5. Lu. 6. Tul. 7. Tere. 8. Tol. 9. Le•• 10. At. 11. Tul. 12. Clet. 13. Cret. 14. Tur. 15. Tur. 16. Le (A. sig∣nifying an oblique Angle. E. the Perpen¦dicular U. the subten∣dent C. I∣nitiall, the complemēt of a side to a quadrant ••. finall, the side conti∣nued to the Radius or a Quadrant. I. left. R. right. and T. one of the top Tri¦angles of the Scheme) it is evidenced in what part of the Diagram the Analo∣gy of my of the 16. Moods be∣gins, which being once knowne, the pro∣gressive sequence of the pro∣portiona∣ble Sides & Angles is easily discerned out of the orderly in volutions of the Fi∣gure it selfe. Here it is to be ob∣served, that as the Book ex∣plaineth the Trisso∣tetral Ta∣ble: so this Trigono∣diatyposis unfoldeth▪ all the in∣tricate dif∣ficulties of the Book.

    • Loxogonosphericals. 12.

      That the Schemes and Types of Triangulary A∣nalogies are not seated in the roomes, where they are treated of, I purposely have done it; to the end, that being all perceived at one view, their multi∣plicity (which would ap∣peare confused in their ••ispersed method) might ••••ot any way discourage 〈…〉〈…〉 der: besides that, this their ••eing together in their ••u•• order, and rancked ••ecording to the exigence of the Sides or Angles, is such a furtherance to the memory, and illustration to the judgement, that it maketh Trigonometry, which of all Sciences was accounted the abstrusest, to be in effect the most 〈◊〉〈◊〉 and 〈◊〉〈◊〉.

      • Monurgeticks. 4
        • 1 Lamaneprep.
          [illustration]
        • 2 Menerolo.
          [illustration]
        • 3 Nerelema.
          [illustration]
        • 4 Ralam••••••
          [illustration]
      • ...

• ...
  • ...
    • ...
      • Of the Disergeticks there be 8. Moods, each whereof is divided into foure Cases.
        • A∣ha∣leb∣ma∣ne.
          • 1. A∣la∣m¦eb∣na
            • Dasimforaug.
              [illustration]
            • Dadisfo••••ug.
              [illustration]
            • Dadisgatin.
              [illustration]
            • Simomatin.
              [illustration]
          • 2. A∣la∣m|eb∣ne.
            • Dasimforauxy.
              [illustration]
            • Dadiscracforeug.
              [illustration]
            • Dadiscramgatin.
              [illustration]
            • Simomatin.
              [illustration]
        • A∣ha∣m|ep∣na∣re.
          • ...〈…〉〈…〉
            • Dadissepamforaur.
              [illustration]
            • Dadissexamforeur.
              [illustration]
            • Dasimatin.
              [illustration]
            • Simomatin.
              [illustration]
          • 4. A¦m∣m¦a∣ne¦p∣re¦la
            • Dadissepamfor.
              [illustration]
            • Dadisse••amfor.
              [illustration]
            • Dasimin.
              [illustration]
            • Simomatin.
              [illustration]
        • E∣he∣n|ab∣ro∣le.
          • ...〈…〉〈…〉
            • Dacramfor.
              [illustration]
            • Damracfor.
              [illustration]
            • Dasimquzin.
              [illustration]
            • Simomatin.
              [illustration]
          • 6. E••¦ne¦ra¦l••∣la.
            • Dacforamb.
              [illustration]
            • Damforac.
              [illustration]
            • Da••imat••m.
              [illustration]
            • Simomatin.
              [illustration]
        • E∣he∣ro∣lab¦me
          • ...〈…〉〈…〉
            • Dacracforeur.
              [illustration]
            • Dambracforeur.
              [illustration]
            • Dacrambatin.
              [illustration]
            • Simomatin.
              [illustration]
          • 8. E••¦re∣lo∣me
            • Dakyxamfor.
              [illustration]
            • Dambyxamfor.
              [illustration]
            • Dakypambin.
              [illustration]
            • Simomatin.
              [illustration]